%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA171-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 06:34:23 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.35s
% Output : Proof 2.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA171-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:59:08 EDT 2026
% 0.15/0.32 % CPUTime :
% 1.14/1.35 % SZS status Unsatisfiable
% 1.14/1.35 % SZS output start Proof
% 1.14/1.35 tff(b_type, type, (
% 1.14/1.35 b: ( $i * $i ) > $o)).
% 1.14/1.35 tff(s_type, type, (
% 1.14/1.35 s: $i > $i)).
% 1.14/1.35 tff(z_type, type, (
% 1.14/1.35 z: $i)).
% 1.14/1.35 tff(r_type, type, (
% 1.14/1.35 r: ( $i * $i ) > $o)).
% 1.14/1.35 tff(inj_0_type, type, (
% 1.14/1.35 inj_0: $i > $i)).
% 1.14/1.35 tff(elem_1_type, type, (
% 1.14/1.35 elem_1: $i)).
% 1.14/1.35 tff(1,assumption,(b(s(z), z)), introduced(assumption)).
% 1.14/1.35 tff(2,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.35 tff(3,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.35 tff(4,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.35 tff(5,plain,
% 1.14/1.35 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(6,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(8,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.14/1.35 tff(9,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.14/1.35 tff(10,plain,(
% 1.14/1.35 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.35 inference(skolemize,[status(sab)],[9])).
% 1.14/1.35 tff(11,plain,
% 1.14/1.35 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.14/1.35 tff(12,plain,
% 1.14/1.35 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[11, 5])).
% 1.14/1.35 tff(13,plain,
% 1.14/1.35 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(14,plain,
% 1.14/1.35 (inj_0(s(z)) = z),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[13, 12])).
% 1.14/1.35 tff(15,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.14/1.35 tff(16,plain,
% 1.14/1.35 (s(z) = s(s(s(z)))),
% 1.14/1.35 inference(symmetry,[status(thm)],[15])).
% 1.14/1.35 tff(17,plain,
% 1.14/1.35 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[16])).
% 1.14/1.35 tff(18,plain,
% 1.14/1.35 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[17])).
% 1.14/1.35 tff(19,plain,
% 1.14/1.35 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(20,plain,
% 1.14/1.35 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[19, 12])).
% 1.14/1.35 tff(21,plain,
% 1.14/1.35 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[20])).
% 1.14/1.35 tff(22,plain,
% 1.14/1.35 (s(s(z)) = z),
% 1.14/1.35 inference(transitivity,[status(thm)],[21, 18, 14])).
% 1.14/1.35 tff(23,plain,
% 1.14/1.35 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.14/1.35 inference(bind,[status(th)],[])).
% 1.14/1.35 tff(24,plain,
% 1.14/1.35 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.35 inference(quant_intro,[status(thm)],[23])).
% 1.14/1.35 tff(25,plain,
% 1.14/1.35 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(26,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.14/1.35 tff(27,plain,
% 1.14/1.35 (![X: $i] : (~(s(X) = z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.14/1.35 tff(28,plain,(
% 1.14/1.35 ![X: $i] : (~(s(X) = z))),
% 1.14/1.35 inference(skolemize,[status(sab)],[27])).
% 1.14/1.35 tff(29,plain,
% 1.14/1.35 (![X: $i] : (~(s(X) = z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.14/1.35 tff(30,plain,
% 1.14/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(31,plain,
% 1.14/1.35 (~(s(s(z)) = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.14/1.35 tff(32,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[31, 22])).
% 1.14/1.35 tff(33,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(34,plain,
% 1.14/1.35 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.35 inference(bind,[status(th)],[])).
% 1.14/1.35 tff(35,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(quant_intro,[status(thm)],[34])).
% 1.14/1.35 tff(36,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(37,plain,
% 1.14/1.35 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.35 inference(bind,[status(th)],[])).
% 1.14/1.35 tff(38,plain,
% 1.14/1.35 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(quant_intro,[status(thm)],[37])).
% 1.14/1.35 tff(39,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.14/1.35 tff(40,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.14/1.35 tff(41,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.14/1.35 tff(42,plain,(
% 1.14/1.35 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(skolemize,[status(sab)],[41])).
% 1.14/1.35 tff(43,plain,
% 1.14/1.35 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.14/1.35 tff(44,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(45,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(46,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.14/1.35 tff(47,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[46, 43, 33, 3, 4])).
% 1.14/1.35 tff(48,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(49,plain,
% 1.14/1.35 (r(s(s(s(z))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[48, 3])).
% 1.14/1.35 tff(50,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.14/1.35 tff(51,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.14/1.35 tff(52,plain,
% 1.14/1.35 (s(elem!1) = s(z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[51])).
% 1.14/1.35 tff(53,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[50, 52])).
% 1.14/1.35 tff(54,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(55,plain,
% 1.14/1.35 (~(s(z) = s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[54, 50])).
% 1.14/1.35 tff(56,assumption,(z = elem!1), introduced(assumption)).
% 1.14/1.35 tff(57,plain,
% 1.14/1.35 (s(z) = s(elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[56])).
% 1.14/1.35 tff(58,plain,
% 1.14/1.35 (s(elem!1) = s(z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[57])).
% 1.14/1.35 tff(59,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[50, 58])).
% 1.14/1.35 tff(60,plain,((~(z = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(61,plain,
% 1.14/1.35 (~(z = elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[60, 50])).
% 1.14/1.35 tff(62,plain,
% 1.14/1.35 ((elem!1 = z) <=> (z = elem!1)),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(63,assumption,(elem!1 = z), introduced(assumption)).
% 1.14/1.35 tff(64,plain,
% 1.14/1.35 (z = elem!1),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.14/1.35 tff(65,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.14/1.35 tff(66,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[65, 64])).
% 1.14/1.35 tff(67,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(68,plain,
% 1.14/1.35 (~(elem!1 = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[67, 61])).
% 1.14/1.35 tff(69,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.14/1.35 tff(70,plain,
% 1.14/1.35 ((z = s(z)) <=> (s(z) = z)),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(71,plain,
% 1.14/1.35 ((s(z) = z) <=> (z = s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[70])).
% 1.14/1.35 tff(72,plain,
% 1.14/1.35 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[71])).
% 1.14/1.35 tff(73,plain,
% 1.14/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(74,plain,
% 1.14/1.35 (~(s(z) = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[73, 29])).
% 1.14/1.35 tff(75,plain,
% 1.14/1.36 (~(z = s(z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[74, 72])).
% 1.14/1.36 tff(76,plain,
% 1.14/1.36 (((~![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)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(77,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(78,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.14/1.36 tff(79,plain,
% 1.14/1.36 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[78, 43])).
% 1.14/1.36 tff(80,plain,
% 1.14/1.36 (b(z, s(z)) | r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[79, 75])).
% 1.14/1.36 tff(81,plain,
% 1.14/1.36 (r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[80, 69])).
% 1.14/1.36 tff(82,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(83,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.14/1.36 tff(84,plain,
% 1.14/1.36 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[83])).
% 1.14/1.36 tff(85,plain,
% 1.14/1.36 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[84])).
% 1.14/1.36 tff(86,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(87,plain,
% 1.14/1.36 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[86, 12])).
% 1.14/1.36 tff(88,plain,
% 1.14/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[83])).
% 1.14/1.36 tff(89,plain,
% 1.14/1.36 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[88])).
% 1.14/1.36 tff(90,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(91,plain,
% 1.14/1.36 (inj_0(s(elem!1)) = elem!1),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[90, 12])).
% 1.14/1.36 tff(92,plain,
% 1.14/1.36 (elem!1 = inj_0(s(elem!1))),
% 1.14/1.36 inference(symmetry,[status(thm)],[91])).
% 1.14/1.36 tff(93,plain,
% 1.14/1.36 (elem!1 = s(s(s(s(elem!1))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[92, 89, 87, 85])).
% 1.14/1.36 tff(94,plain,
% 1.14/1.36 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[93])).
% 1.14/1.36 tff(95,plain,
% 1.14/1.36 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[94])).
% 1.14/1.36 tff(96,plain,
% 1.14/1.36 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[95])).
% 1.14/1.36 tff(97,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(98,plain,
% 1.14/1.36 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[97, 12])).
% 1.14/1.36 tff(99,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(100,plain,
% 1.14/1.36 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[99])).
% 1.14/1.36 tff(101,plain,
% 1.14/1.36 (s(s(z)) = s(s(s(elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[21, 100, 98])).
% 1.14/1.36 tff(102,plain,
% 1.14/1.36 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[101])).
% 1.14/1.36 tff(103,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(104,plain,
% 1.14/1.36 (inj_0(s(s(z))) = s(z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[103, 12])).
% 1.14/1.36 tff(105,plain,
% 1.14/1.36 (s(z) = inj_0(s(s(z)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[104])).
% 1.14/1.36 tff(106,plain,
% 1.14/1.36 (s(z) = s(s(elem!1))),
% 1.14/1.36 inference(transitivity,[status(thm)],[105, 102, 87])).
% 1.14/1.36 tff(107,plain,
% 1.14/1.36 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[106])).
% 1.14/1.36 tff(108,plain,
% 1.14/1.36 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.14/1.36 inference(symmetry,[status(thm)],[107])).
% 1.14/1.36 tff(109,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(110,plain,
% 1.14/1.36 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[109, 12])).
% 1.14/1.36 tff(111,plain,
% 1.14/1.36 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[110])).
% 1.14/1.36 tff(112,plain,
% 1.14/1.36 (s(elem!1) = z),
% 1.14/1.36 inference(transitivity,[status(thm)],[111, 108, 14])).
% 1.14/1.36 tff(113,plain,
% 1.14/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(114,plain,
% 1.14/1.36 (~(s(elem!1) = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[113, 29])).
% 1.14/1.36 tff(115,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[114, 112])).
% 1.14/1.36 tff(116,plain,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(117,plain,
% 1.14/1.36 (~(s(s(s(z))) = elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[116, 96])).
% 1.14/1.36 tff(118,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.36 tff(119,plain,
% 1.14/1.36 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(120,plain,
% 1.14/1.36 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[119])).
% 1.14/1.36 tff(121,plain,
% 1.14/1.36 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[87])).
% 1.14/1.36 tff(122,plain,
% 1.14/1.36 (s(s(s(s(elem!1)))) = elem!1),
% 1.14/1.36 inference(transitivity,[status(thm)],[84, 121, 88, 91])).
% 1.14/1.36 tff(123,plain,
% 1.14/1.36 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[122])).
% 1.14/1.36 tff(124,plain,
% 1.14/1.36 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.14/1.36 inference(transitivity,[status(thm)],[123, 120])).
% 1.14/1.36 tff(125,plain,
% 1.14/1.36 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[124])).
% 1.14/1.36 tff(126,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.14/1.36 tff(127,plain,
% 1.14/1.36 (s(z) = s(s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[126])).
% 1.14/1.36 tff(128,plain,
% 1.14/1.36 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[127])).
% 1.14/1.36 tff(129,plain,
% 1.14/1.36 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.14/1.36 inference(symmetry,[status(thm)],[128])).
% 1.14/1.36 tff(130,plain,
% 1.14/1.36 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[98])).
% 1.14/1.36 tff(131,plain,
% 1.14/1.36 (s(s(s(elem!1))) = z),
% 1.14/1.36 inference(transitivity,[status(thm)],[130, 129, 14])).
% 1.14/1.36 tff(132,plain,
% 1.14/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(133,plain,
% 1.14/1.36 (~(s(s(s(elem!1))) = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[132, 29])).
% 1.14/1.36 tff(134,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[133, 131])).
% 1.14/1.36 tff(135,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(136,plain,
% 1.14/1.36 (~(s(z) = elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[135, 125])).
% 1.14/1.36 tff(137,plain,
% 1.14/1.36 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[83])).
% 1.14/1.36 tff(138,plain,
% 1.14/1.36 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(139,plain,
% 1.14/1.36 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[138])).
% 1.14/1.36 tff(140,plain,
% 1.14/1.36 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[139])).
% 1.14/1.36 tff(141,plain,
% 1.14/1.36 (~(z = s(s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[133, 140])).
% 1.14/1.36 tff(142,plain,
% 1.14/1.36 (((~![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)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(143,plain,
% 1.14/1.36 ((~![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)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(144,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.14/1.36 tff(145,plain,
% 1.14/1.36 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[144, 43])).
% 1.14/1.36 tff(146,plain,
% 1.14/1.36 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[145, 141])).
% 1.14/1.36 tff(147,plain,
% 1.14/1.36 (r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[146, 82])).
% 1.14/1.36 tff(148,plain,
% 1.14/1.36 (r(z, s(elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[147, 137])).
% 1.14/1.36 tff(149,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.14/1.36 tff(150,plain,
% 1.14/1.36 (s(s(z)) = s(s(elem!1))),
% 1.14/1.36 inference(transitivity,[status(thm)],[149, 92, 89, 87])).
% 1.14/1.36 tff(151,plain,
% 1.14/1.36 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[150])).
% 1.14/1.36 tff(152,plain,
% 1.14/1.36 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[151])).
% 1.14/1.36 tff(153,plain,
% 1.14/1.36 (s(elem!1) = s(z)),
% 1.14/1.36 inference(transitivity,[status(thm)],[111, 152, 104])).
% 1.14/1.36 tff(154,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[50, 153])).
% 1.14/1.36 tff(155,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(156,plain,
% 1.14/1.36 (~(s(s(z)) = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[155, 83, 50])).
% 1.14/1.36 tff(157,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.14/1.36 tff(158,plain,
% 1.14/1.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.14/1.36 inference(transitivity,[status(thm)],[157, 92, 89, 87])).
% 1.14/1.36 tff(159,plain,
% 1.14/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[158])).
% 1.14/1.36 tff(160,plain,
% 1.14/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(161,plain,
% 1.14/1.36 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[160, 12])).
% 1.14/1.36 tff(162,plain,
% 1.14/1.36 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[161])).
% 1.14/1.36 tff(163,plain,
% 1.14/1.36 (s(s(s(z))) = s(elem!1)),
% 1.14/1.36 inference(transitivity,[status(thm)],[162, 159, 110])).
% 1.14/1.36 tff(164,plain,
% 1.14/1.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[163])).
% 1.14/1.36 tff(165,plain,
% 1.14/1.36 (s(s(z)) = s(s(elem!1))),
% 1.14/1.36 inference(transitivity,[status(thm)],[21, 164, 89, 87])).
% 1.14/1.36 tff(166,plain,
% 1.14/1.36 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[165])).
% 1.14/1.36 tff(167,plain,
% 1.14/1.36 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[166])).
% 1.14/1.36 tff(168,plain,
% 1.14/1.36 (s(elem!1) = s(z)),
% 1.14/1.36 inference(transitivity,[status(thm)],[111, 167, 104])).
% 1.14/1.36 tff(169,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[50, 168])).
% 1.14/1.36 tff(170,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(171,plain,
% 1.14/1.36 (~(s(s(s(s(z)))) = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[170, 83, 50])).
% 1.14/1.36 tff(172,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.14/1.36 tff(173,assumption,(r(z, s(z))), introduced(assumption)).
% 1.14/1.36 tff(174,plain,
% 1.14/1.36 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(175,plain,
% 1.14/1.36 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[174])).
% 1.14/1.36 tff(176,plain,
% 1.14/1.36 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[175])).
% 1.14/1.36 tff(177,plain,
% 1.14/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(178,plain,
% 1.14/1.36 (~(s(s(s(z))) = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[177, 29])).
% 1.14/1.36 tff(179,plain,
% 1.14/1.36 (~(z = s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[178, 176])).
% 1.14/1.36 tff(180,plain,
% 1.14/1.36 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.14/1.36 inference(bind,[status(th)],[])).
% 1.14/1.36 tff(181,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(quant_intro,[status(thm)],[180])).
% 1.14/1.36 tff(182,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(183,plain,
% 1.14/1.36 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.14/1.36 inference(bind,[status(th)],[])).
% 1.14/1.36 tff(184,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(quant_intro,[status(thm)],[183])).
% 1.14/1.36 tff(185,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.14/1.36 tff(186,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.14/1.36 tff(187,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[186, 182])).
% 1.14/1.36 tff(188,plain,(
% 1.14/1.36 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(skolemize,[status(sab)],[187])).
% 1.14/1.36 tff(189,plain,
% 1.14/1.36 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[188, 181])).
% 1.14/1.36 tff(190,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(191,plain,
% 1.14/1.36 (((~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))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(192,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[191])).
% 1.14/1.36 tff(193,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[192, 190])).
% 1.14/1.36 tff(194,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(195,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.14/1.36 tff(196,plain,
% 1.14/1.36 (~r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[195, 189, 173, 118])).
% 1.14/1.36 tff(197,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(198,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(199,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.14/1.36 tff(200,plain,
% 1.14/1.36 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[199, 43, 196])).
% 1.14/1.36 tff(201,plain,
% 1.14/1.36 (b(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[200, 179])).
% 1.14/1.36 tff(202,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.14/1.36 tff(203,plain,
% 1.14/1.36 (s(z) = s(s(s(elem!1)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[202])).
% 1.14/1.36 tff(204,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.36 tff(205,plain,
% 1.14/1.36 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[204])).
% 1.14/1.36 tff(206,plain,
% 1.14/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.14/1.36 inference(symmetry,[status(thm)],[205])).
% 1.14/1.36 tff(207,plain,
% 1.14/1.36 (s(s(elem!1)) = z),
% 1.14/1.36 inference(transitivity,[status(thm)],[121, 206, 14])).
% 1.14/1.36 tff(208,plain,
% 1.14/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(209,plain,
% 1.14/1.36 (~(s(s(elem!1)) = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[208, 29])).
% 1.14/1.36 tff(210,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[209, 207])).
% 1.14/1.36 tff(211,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(212,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[211, 203])).
% 1.14/1.36 tff(213,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(214,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.14/1.36 tff(215,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(216,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(217,plain,
% 1.14/1.36 (((~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))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(218,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[217])).
% 1.14/1.36 tff(219,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[218, 216])).
% 1.14/1.36 tff(220,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(221,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.14/1.36 tff(222,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[221, 189, 215, 173, 214])).
% 1.14/1.36 tff(223,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(224,plain,
% 1.14/1.36 (~r(s(s(s(elem!1))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[223, 173, 147])).
% 1.14/1.36 tff(225,plain,
% 1.14/1.36 (((~![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)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(226,plain,
% 1.14/1.36 ((~![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)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(227,plain,
% 1.14/1.36 ((~![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))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.14/1.36 tff(228,plain,
% 1.14/1.36 (b(s(s(s(elem!1))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[227, 43, 224, 213])).
% 1.14/1.36 tff(229,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(230,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.14/1.36 tff(231,plain,
% 1.14/1.36 (s(elem!1) = s(s(z))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[230])).
% 1.14/1.36 tff(232,plain,
% 1.14/1.36 (s(s(elem!1)) = s(s(s(z)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[231])).
% 1.14/1.36 tff(233,plain,
% 1.14/1.36 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[232])).
% 1.14/1.36 tff(234,plain,
% 1.14/1.36 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[233])).
% 1.14/1.36 tff(235,plain,
% 1.14/1.36 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.14/1.36 inference(symmetry,[status(thm)],[234])).
% 1.14/1.36 tff(236,plain,
% 1.14/1.36 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[235])).
% 1.14/1.36 tff(237,plain,
% 1.14/1.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[230])).
% 1.14/1.36 tff(238,plain,
% 1.14/1.36 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[237])).
% 1.14/1.36 tff(239,plain,
% 1.14/1.36 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[229, 238])).
% 1.14/1.36 tff(240,plain,
% 1.14/1.36 (~b(s(s(s(elem!1))), s(z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[239, 236])).
% 1.14/1.36 tff(241,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.14/1.36 tff(242,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[241, 240])).
% 1.14/1.36 tff(243,plain,((~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(244,plain,
% 1.14/1.36 (~(elem!1 = s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[243, 229, 228])).
% 1.14/1.36 tff(245,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.14/1.36 tff(246,plain,
% 1.14/1.36 (elem!1 = s(z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[245, 119])).
% 1.14/1.36 tff(247,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.14/1.36 tff(248,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[247, 246])).
% 1.14/1.36 tff(249,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(250,plain,
% 1.14/1.36 (~(s(z) = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[249, 244])).
% 1.14/1.36 tff(251,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.14/1.36 tff(252,plain,
% 1.14/1.36 (s(s(elem!1)) = s(elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[251])).
% 1.14/1.36 tff(253,plain,
% 1.14/1.36 (s(s(elem!1)) = elem!1),
% 1.14/1.36 inference(transitivity,[status(thm)],[252, 251])).
% 1.14/1.36 tff(254,plain,
% 1.14/1.36 (s(s(s(elem!1))) = s(elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[253])).
% 1.14/1.36 tff(255,plain,
% 1.14/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[254])).
% 1.14/1.36 tff(256,plain,
% 1.14/1.36 (elem!1 = s(elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[251])).
% 1.14/1.36 tff(257,plain,
% 1.14/1.36 (elem!1 = s(s(s(elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[256, 255])).
% 1.14/1.36 tff(258,plain,
% 1.14/1.36 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(259,plain,
% 1.14/1.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[251])).
% 1.14/1.36 tff(260,plain,
% 1.14/1.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[259, 258])).
% 1.14/1.36 tff(261,plain,
% 1.14/1.36 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[260])).
% 1.14/1.36 tff(262,plain,
% 1.14/1.36 (~(elem!1 = s(s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[172, 261])).
% 1.14/1.36 tff(263,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[262, 257])).
% 1.14/1.36 tff(264,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(265,plain,
% 1.14/1.36 (~(s(elem!1) = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[264, 172])).
% 1.14/1.36 tff(266,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(267,plain,
% 1.14/1.36 (((~![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))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(268,plain,
% 1.14/1.36 ((~![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))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(269,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.14/1.36 tff(270,plain,
% 1.14/1.36 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[269, 43])).
% 1.14/1.36 tff(271,plain,
% 1.14/1.36 (r(s(elem!1), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[270, 266, 265])).
% 1.14/1.36 tff(272,plain,
% 1.14/1.36 (~(s(z) = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[249, 247])).
% 1.14/1.36 tff(273,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(274,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.14/1.36 tff(275,assumption,(r(s(z), z)), introduced(assumption)).
% 1.14/1.36 tff(276,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.14/1.36 tff(277,plain,
% 1.14/1.36 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[258])).
% 1.14/1.36 tff(278,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.36 tff(279,plain,
% 1.14/1.36 (s(s(s(elem!1))) = elem!1),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.14/1.36 tff(280,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[276, 279])).
% 1.14/1.36 tff(281,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(282,plain,
% 1.14/1.36 (~(elem!1 = s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[281, 276])).
% 1.14/1.36 tff(283,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(284,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(285,plain,
% 1.14/1.36 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(286,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[285])).
% 1.14/1.36 tff(287,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[286, 284])).
% 1.14/1.36 tff(288,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(289,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[288, 287])).
% 1.14/1.36 tff(290,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[289, 189, 274, 283, 215])).
% 1.14/1.36 tff(291,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(292,plain,
% 1.14/1.36 (~r(elem!1, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[291, 147, 274])).
% 1.14/1.36 tff(293,plain,
% 1.14/1.36 (((~![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)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(294,plain,
% 1.14/1.37 ((~![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)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(295,plain,
% 1.14/1.37 ((~![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))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.14/1.37 tff(296,plain,
% 1.14/1.37 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[295, 43, 292])).
% 1.14/1.37 tff(297,plain,
% 1.14/1.37 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[296, 282])).
% 1.14/1.37 tff(298,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(299,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(300,plain,
% 1.14/1.37 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(301,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[300])).
% 1.14/1.37 tff(302,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[301, 299])).
% 1.14/1.37 tff(303,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(304,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.14/1.37 tff(305,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[304, 189, 215, 275, 298])).
% 1.14/1.37 tff(306,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(307,plain,
% 1.14/1.37 (~r(s(z), s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[306, 147, 275])).
% 1.14/1.37 tff(308,plain,
% 1.14/1.37 (((~![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)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(309,plain,
% 1.14/1.37 ((~![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)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(310,plain,
% 1.14/1.37 ((~![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))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.14/1.37 tff(311,plain,
% 1.14/1.37 (b(s(z), s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[310, 43, 211, 307])).
% 1.14/1.37 tff(312,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(313,plain,
% 1.14/1.37 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(314,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[313])).
% 1.14/1.37 tff(315,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[314, 312])).
% 1.14/1.37 tff(316,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(317,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.14/1.37 tff(318,plain,
% 1.14/1.37 (~r(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[317, 189, 274, 275])).
% 1.14/1.37 tff(319,plain,
% 1.14/1.37 (((~![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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(320,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(321,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.14/1.37 tff(322,plain,
% 1.14/1.37 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[321, 43])).
% 1.14/1.37 tff(323,plain,
% 1.14/1.37 (b(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[322, 247, 318])).
% 1.14/1.37 tff(324,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(325,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(326,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.14/1.37 tff(327,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.14/1.37 tff(328,plain,
% 1.14/1.37 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.14/1.37 inference(bind,[status(th)],[])).
% 1.14/1.37 tff(329,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(quant_intro,[status(thm)],[328])).
% 1.14/1.37 tff(330,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(331,plain,
% 1.14/1.37 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(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(X1, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, 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(X1, X4))) <=> ((~b(X1, 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(X1, X4))) | (~b(X3, X4))) <=> (((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, 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(X1, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.14/1.37 inference(bind,[status(th)],[])).
% 1.14/1.37 tff(332,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(quant_intro,[status(thm)],[331])).
% 1.14/1.37 tff(333,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.14/1.37 tff(334,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.14/1.37 tff(335,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[334, 330])).
% 1.14/1.37 tff(336,plain,(
% 1.14/1.37 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(skolemize,[status(sab)],[335])).
% 1.14/1.37 tff(337,plain,
% 1.14/1.37 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[336, 329])).
% 1.14/1.37 tff(338,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(339,plain,
% 1.14/1.37 (((~b(elem!1, s(s(s(elem!1))))) | (~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(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(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(340,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~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(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(X1, 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(s(s(elem!1))))) | (~b(elem!1, s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[339])).
% 1.14/1.37 tff(341,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~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(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(X1, 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(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[340, 338])).
% 1.14/1.37 tff(342,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(343,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.14/1.37 tff(344,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[343, 337, 327, 326, 325, 324])).
% 1.14/1.37 tff(345,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(346,plain,
% 1.14/1.37 (~b(s(s(s(elem!1))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[345, 323, 311, 297])).
% 1.14/1.37 tff(347,plain,
% 1.14/1.37 (((~![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))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(348,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(349,plain,
% 1.14/1.37 ((~![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)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.14/1.37 tff(350,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[349, 43])).
% 1.14/1.37 tff(351,plain,
% 1.14/1.37 (r(s(s(s(elem!1))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[350, 346, 276])).
% 1.14/1.37 tff(352,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.14/1.37 tff(353,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.37 tff(354,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(355,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(356,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.14/1.37 tff(357,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[356, 189, 353, 273, 352])).
% 1.14/1.37 tff(358,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(359,plain,
% 1.14/1.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[358, 351, 273])).
% 1.14/1.37 tff(360,plain,
% 1.14/1.37 (((~![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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(361,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(362,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.14/1.37 tff(363,plain,
% 1.14/1.37 ((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))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[362, 43])).
% 1.14/1.37 tff(364,plain,
% 1.14/1.37 (b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[363, 359, 172])).
% 1.14/1.37 tff(365,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.37 tff(366,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(367,plain,
% 1.14/1.37 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[366])).
% 1.14/1.37 tff(368,plain,
% 1.14/1.37 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[367])).
% 1.14/1.37 tff(369,plain,
% 1.14/1.37 (~(s(s(s(elem!1))) = s(z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[211, 368])).
% 1.14/1.37 tff(370,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.14/1.37 tff(371,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(372,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(373,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.14/1.37 tff(374,plain,
% 1.14/1.37 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[373, 189])).
% 1.14/1.37 tff(375,plain,
% 1.14/1.37 (~r(s(elem!1), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[374, 370, 273])).
% 1.14/1.37 tff(376,plain,
% 1.14/1.37 (((~![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))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(377,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(378,plain,
% 1.14/1.37 ((~![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)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.14/1.37 tff(379,plain,
% 1.14/1.37 (b(s(elem!1), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[378, 43, 114, 375])).
% 1.14/1.37 tff(380,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(381,plain,
% 1.14/1.37 (((~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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(382,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[381])).
% 1.14/1.37 tff(383,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[382, 380])).
% 1.14/1.37 tff(384,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(385,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.14/1.37 tff(386,plain,
% 1.14/1.37 (~r(z, s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[385, 189, 370, 273])).
% 1.14/1.37 tff(387,plain,
% 1.14/1.37 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(388,plain,
% 1.14/1.37 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.14/1.37 inference(symmetry,[status(thm)],[387])).
% 1.14/1.37 tff(389,plain,
% 1.14/1.37 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[388])).
% 1.14/1.37 tff(390,plain,
% 1.14/1.37 (~(z = s(elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[114, 389])).
% 1.14/1.37 tff(391,plain,
% 1.14/1.37 (((~![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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(392,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(393,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.14/1.37 tff(394,plain,
% 1.14/1.37 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[393, 43])).
% 1.14/1.37 tff(395,plain,
% 1.14/1.37 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[394, 390])).
% 1.14/1.37 tff(396,plain,
% 1.14/1.37 (b(z, s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[395, 386])).
% 1.14/1.37 tff(397,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(398,plain,
% 1.14/1.37 (((~b(z, s(elem!1))) | (~b(z, s(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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(399,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[398])).
% 1.14/1.38 tff(400,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[399, 397])).
% 1.14/1.38 tff(401,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(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)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(402,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.14/1.38 tff(403,plain,
% 1.14/1.38 (~b(s(s(s(elem!1))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[402, 337, 365, 396, 379])).
% 1.14/1.38 tff(404,plain,
% 1.14/1.38 (((~![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))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(405,plain,
% 1.14/1.38 ((~![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))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(406,plain,
% 1.14/1.38 ((~![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)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.14/1.38 tff(407,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[406, 43, 133, 403])).
% 1.14/1.38 tff(408,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(409,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(410,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.14/1.38 tff(411,plain,
% 1.14/1.38 (~r(s(s(s(elem!1))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[410, 189, 407, 275])).
% 1.14/1.38 tff(412,plain,
% 1.14/1.38 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[227, 43, 411])).
% 1.14/1.38 tff(413,plain,
% 1.14/1.38 (b(s(s(s(elem!1))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[412, 369])).
% 1.14/1.38 tff(414,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(415,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(416,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.14/1.38 tff(417,plain,
% 1.14/1.38 (~r(s(z), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[416, 189, 274, 275])).
% 1.14/1.38 tff(418,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(419,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(420,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[419, 418])).
% 1.14/1.38 tff(421,plain,
% 1.14/1.38 (~r(s(z), s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[420, 189, 407, 275])).
% 1.14/1.38 tff(422,plain,
% 1.14/1.38 (b(s(z), s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[310, 43, 211, 421])).
% 1.14/1.38 tff(423,plain,
% 1.14/1.38 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(424,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.38 tff(425,plain,
% 1.14/1.38 (s(s(s(elem!1))) = s(elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.14/1.38 tff(426,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[172, 425])).
% 1.14/1.38 tff(427,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(428,plain,
% 1.14/1.38 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[427, 172])).
% 1.14/1.38 tff(429,plain,
% 1.14/1.38 (s(s(z)) = s(elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[245])).
% 1.14/1.38 tff(430,plain,
% 1.14/1.38 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[429])).
% 1.14/1.38 tff(431,plain,
% 1.14/1.38 (s(s(elem!1)) = s(s(s(z)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[430])).
% 1.14/1.38 tff(432,plain,
% 1.14/1.38 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[430])).
% 1.14/1.38 tff(433,plain,
% 1.14/1.38 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[432])).
% 1.14/1.38 tff(434,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[433, 431])).
% 1.14/1.38 tff(435,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[434])).
% 1.14/1.38 tff(436,plain,
% 1.14/1.38 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[433, 431])).
% 1.14/1.38 tff(437,plain,
% 1.14/1.38 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[436])).
% 1.14/1.38 tff(438,plain,
% 1.14/1.38 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[431])).
% 1.14/1.38 tff(439,plain,
% 1.14/1.38 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.38 inference(symmetry,[status(thm)],[438])).
% 1.14/1.38 tff(440,plain,
% 1.14/1.38 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[439])).
% 1.14/1.38 tff(441,plain,
% 1.14/1.38 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[245])).
% 1.14/1.38 tff(442,plain,
% 1.14/1.38 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[441])).
% 1.14/1.38 tff(443,plain,
% 1.14/1.38 (~(s(s(s(z))) = elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[33, 442])).
% 1.14/1.38 tff(444,plain,
% 1.14/1.38 (~(s(s(elem!1)) = elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[443, 440])).
% 1.14/1.38 tff(445,plain,
% 1.14/1.38 (elem!1 = s(z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[249, 245])).
% 1.14/1.38 tff(446,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.14/1.38 tff(447,plain,
% 1.14/1.38 (s(s(z)) = s(s(s(z)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[446])).
% 1.14/1.38 tff(448,plain,
% 1.14/1.38 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[447])).
% 1.14/1.38 tff(449,plain,
% 1.14/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[448])).
% 1.14/1.38 tff(450,plain,
% 1.14/1.38 (s(elem!1) = s(z)),
% 1.14/1.38 inference(transitivity,[status(thm)],[231, 21, 449, 104])).
% 1.14/1.38 tff(451,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[50, 450])).
% 1.14/1.38 tff(452,plain,((~(s(s(s(z))) = s(s(z)))) | (s(elem!1) = s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(453,plain,
% 1.14/1.38 (~(s(s(s(z))) = s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[452, 445, 50])).
% 1.14/1.38 tff(454,plain,
% 1.14/1.38 (s(elem!1) = s(s(z))),
% 1.14/1.38 inference(symmetry,[status(thm)],[429])).
% 1.14/1.38 tff(455,plain,
% 1.14/1.38 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[431, 454])).
% 1.14/1.38 tff(456,plain,
% 1.14/1.38 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.14/1.38 inference(symmetry,[status(thm)],[455])).
% 1.14/1.38 tff(457,plain,
% 1.14/1.38 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[456])).
% 1.14/1.38 tff(458,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 1.14/1.38 tff(459,plain,
% 1.14/1.38 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.14/1.38 tff(460,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.14/1.38 tff(461,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(462,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(463,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.14/1.38 tff(464,plain,
% 1.14/1.38 (~r(s(s(elem!1)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[463, 189, 370, 460])).
% 1.14/1.38 tff(465,plain,
% 1.14/1.38 (((~![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))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(466,plain,
% 1.14/1.38 ((~![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))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(467,plain,
% 1.14/1.38 ((~![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)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.14/1.38 tff(468,plain,
% 1.14/1.38 (b(s(s(elem!1)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[467, 43, 209, 464])).
% 1.14/1.38 tff(469,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(470,plain,
% 1.14/1.38 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(471,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, 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(X1, 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(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[470])).
% 1.14/1.38 tff(472,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, 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(X1, 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(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[471, 469])).
% 1.14/1.38 tff(473,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(474,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.14/1.38 tff(475,plain,
% 1.14/1.38 (~b(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[474, 337, 396, 379, 468])).
% 1.14/1.38 tff(476,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(477,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(478,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.14/1.38 tff(479,plain,
% 1.14/1.38 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[478, 189, 273, 460])).
% 1.14/1.38 tff(480,plain,
% 1.14/1.38 (((~![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)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(481,plain,
% 1.14/1.38 ((~![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)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(482,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.14/1.38 tff(483,plain,
% 1.14/1.38 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[482, 43, 479])).
% 1.14/1.38 tff(484,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[483, 475, 459])).
% 1.14/1.38 tff(485,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(z))) | (~(s(z) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(486,plain,
% 1.14/1.38 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[485, 453, 245, 273, 370])).
% 1.14/1.38 tff(487,plain,
% 1.14/1.38 (((~![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))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(488,plain,
% 1.14/1.38 ((~![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))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(489,plain,
% 1.14/1.38 ((~![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)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.14/1.38 tff(490,plain,
% 1.14/1.38 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[489, 43, 486])).
% 1.14/1.38 tff(491,plain,
% 1.14/1.38 (b(s(s(elem!1)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[490, 444])).
% 1.14/1.38 tff(492,plain,
% 1.14/1.38 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[245])).
% 1.14/1.38 tff(493,plain,
% 1.14/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[324, 492])).
% 1.14/1.38 tff(494,plain,
% 1.14/1.38 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[245])).
% 1.14/1.38 tff(495,plain,
% 1.14/1.38 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[241, 494])).
% 1.14/1.38 tff(496,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(elem!1)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(497,plain,
% 1.14/1.38 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(498,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))), s(s(elem!1))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[497])).
% 1.14/1.38 tff(499,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))), s(s(elem!1)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[498, 496])).
% 1.14/1.38 tff(500,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(501,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(elem!1))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.14/1.38 tff(502,plain,
% 1.14/1.38 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[501, 337, 495, 493, 491])).
% 1.14/1.38 tff(503,plain,
% 1.14/1.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[502, 437])).
% 1.14/1.38 tff(504,plain,
% 1.14/1.38 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(505,plain,
% 1.14/1.38 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[504])).
% 1.14/1.38 tff(506,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(507,plain,
% 1.14/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[506])).
% 1.14/1.38 tff(508,plain,
% 1.14/1.38 (s(s(z)) = s(s(s(s(z))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[21, 507, 161, 506])).
% 1.14/1.38 tff(509,plain,
% 1.14/1.38 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[508])).
% 1.14/1.38 tff(510,plain,
% 1.14/1.38 (s(z) = s(s(s(s(z))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[105, 509, 161, 506])).
% 1.14/1.38 tff(511,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(512,plain,
% 1.14/1.38 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[511])).
% 1.14/1.38 tff(513,plain,
% 1.14/1.38 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.14/1.38 inference(symmetry,[status(thm)],[512])).
% 1.14/1.38 tff(514,plain,
% 1.14/1.38 (s(s(s(z))) = z),
% 1.14/1.38 inference(transitivity,[status(thm)],[162, 513, 14])).
% 1.14/1.38 tff(515,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[178, 514])).
% 1.14/1.38 tff(516,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(517,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[516, 510])).
% 1.14/1.38 tff(518,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(519,plain,
% 1.14/1.38 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[518, 505])).
% 1.14/1.38 tff(520,plain,
% 1.14/1.38 (((~![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)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(521,plain,
% 1.14/1.38 ((~![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)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(522,plain,
% 1.14/1.38 ((~![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))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.14/1.38 tff(523,plain,
% 1.14/1.38 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[522, 43])).
% 1.14/1.38 tff(524,plain,
% 1.14/1.38 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[523, 519])).
% 1.14/1.38 tff(525,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[524, 503])).
% 1.14/1.38 tff(526,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[525, 435])).
% 1.14/1.38 tff(527,plain,
% 1.14/1.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(528,plain,
% 1.14/1.38 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[454, 431])).
% 1.14/1.38 tff(529,plain,
% 1.14/1.38 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[528, 527])).
% 1.14/1.38 tff(530,plain,
% 1.14/1.38 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[529])).
% 1.14/1.38 tff(531,plain,
% 1.14/1.38 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[530])).
% 1.14/1.38 tff(532,plain,
% 1.14/1.38 (~(s(elem!1) = s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[453, 531])).
% 1.14/1.38 tff(533,plain,
% 1.14/1.38 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[430, 432])).
% 1.14/1.38 tff(534,plain,
% 1.14/1.38 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[431, 433])).
% 1.14/1.38 tff(535,plain,
% 1.14/1.38 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[534])).
% 1.14/1.38 tff(536,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(537,plain,
% 1.14/1.38 (((~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(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(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(538,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[537])).
% 1.14/1.38 tff(539,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[538, 536])).
% 1.14/1.39 tff(540,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(541,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.14/1.39 tff(542,plain,
% 1.14/1.39 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[541, 337, 365, 495, 493, 491])).
% 1.14/1.39 tff(543,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[542, 535])).
% 1.14/1.39 tff(544,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(545,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(546,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.14/1.39 tff(547,plain,
% 1.14/1.39 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[546, 43])).
% 1.14/1.39 tff(548,plain,
% 1.14/1.39 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[547, 518])).
% 1.14/1.39 tff(549,plain,
% 1.14/1.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[548, 543])).
% 1.14/1.39 tff(550,plain,
% 1.14/1.39 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[549, 533])).
% 1.14/1.39 tff(551,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(552,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(553,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.14/1.39 tff(554,plain,
% 1.14/1.39 (~r(s(s(elem!1)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[553, 189, 215, 550])).
% 1.14/1.39 tff(555,plain,
% 1.14/1.39 (b(s(s(elem!1)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[467, 43, 209, 554])).
% 1.14/1.39 tff(556,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(557,plain,
% 1.14/1.39 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(558,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, 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(X1, 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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[557])).
% 1.14/1.39 tff(559,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, 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(X1, 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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[558, 556])).
% 1.14/1.39 tff(560,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(561,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.14/1.39 tff(562,plain,
% 1.14/1.39 (~b(s(elem!1), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[561, 337, 396, 379, 555])).
% 1.14/1.39 tff(563,plain,
% 1.14/1.39 (((~![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))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(564,plain,
% 1.14/1.39 ((~![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))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(565,plain,
% 1.14/1.39 ((~![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)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.14/1.39 tff(566,plain,
% 1.14/1.39 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[565, 43, 562])).
% 1.14/1.39 tff(567,plain,
% 1.14/1.39 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[566, 532])).
% 1.14/1.39 tff(568,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(569,plain,
% 1.14/1.39 (((~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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(570,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[569])).
% 1.14/1.39 tff(571,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[570, 568])).
% 1.14/1.39 tff(572,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(573,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.14/1.39 tff(574,plain,
% 1.14/1.39 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[573, 189, 567])).
% 1.14/1.39 tff(575,plain,
% 1.14/1.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[574, 526])).
% 1.14/1.39 tff(576,plain,
% 1.14/1.39 (((~![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)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(577,plain,
% 1.14/1.39 ((~![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)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(578,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.14/1.39 tff(579,plain,
% 1.14/1.39 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[578, 43])).
% 1.14/1.39 tff(580,plain,
% 1.14/1.39 (b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[579, 575, 428])).
% 1.14/1.39 tff(581,plain,
% 1.14/1.39 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[453, 457])).
% 1.14/1.39 tff(582,plain,
% 1.14/1.39 (~b(s(s(elem!1)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[474, 337, 396, 379, 555])).
% 1.14/1.39 tff(583,plain,
% 1.14/1.39 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[482, 43, 582])).
% 1.14/1.39 tff(584,plain,
% 1.14/1.39 (r(s(s(elem!1)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[583, 581])).
% 1.14/1.39 tff(585,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.39 tff(586,plain,
% 1.14/1.39 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.39 inference(transitivity,[status(thm)],[585, 430])).
% 1.14/1.39 tff(587,plain,
% 1.14/1.39 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[586])).
% 1.14/1.39 tff(588,plain,
% 1.14/1.39 (s(s(s(elem!1))) = s(elem!1)),
% 1.14/1.39 inference(transitivity,[status(thm)],[130, 587, 110])).
% 1.14/1.39 tff(589,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[172, 588])).
% 1.14/1.39 tff(590,plain,((~(s(s(s(s(elem!1)))) = s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(591,plain,
% 1.14/1.39 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[590, 245, 172])).
% 1.14/1.39 tff(592,plain,
% 1.14/1.39 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[431])).
% 1.14/1.39 tff(593,plain,
% 1.14/1.39 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[592])).
% 1.14/1.39 tff(594,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), introduced(assumption)).
% 1.14/1.39 tff(595,plain,
% 1.14/1.39 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[431])).
% 1.14/1.39 tff(596,plain,
% 1.14/1.39 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[595])).
% 1.14/1.39 tff(597,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.14/1.39 tff(598,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.14/1.39 tff(599,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.14/1.39 tff(600,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.14/1.39 tff(601,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~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(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(602,plain,
% 1.14/1.39 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(603,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[602])).
% 1.14/1.39 tff(604,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[603, 601])).
% 1.14/1.39 tff(605,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(606,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.14/1.39 tff(607,plain,
% 1.14/1.39 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[606, 337, 600, 599, 598, 597])).
% 1.14/1.39 tff(608,plain,
% 1.14/1.39 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[607, 596])).
% 1.14/1.39 tff(609,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), 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(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(610,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(611,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.14/1.39 tff(612,plain,
% 1.14/1.39 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[611, 43])).
% 1.14/1.39 tff(613,plain,
% 1.14/1.39 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[612, 608, 594])).
% 1.14/1.39 tff(614,plain,
% 1.14/1.39 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[613, 593])).
% 1.14/1.39 tff(615,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.14/1.39 tff(616,plain,
% 1.14/1.39 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.39 inference(commutativity,[status(thm)],[])).
% 1.14/1.39 tff(617,plain,
% 1.14/1.39 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[432])).
% 1.14/1.39 tff(618,plain,
% 1.14/1.39 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[429, 617])).
% 1.14/1.39 tff(619,plain,
% 1.14/1.39 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.39 inference(transitivity,[status(thm)],[618, 616])).
% 1.14/1.39 tff(620,plain,
% 1.14/1.39 ((~(s(s(z)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[619])).
% 1.14/1.39 tff(621,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.39 tff(622,plain,
% 1.14/1.39 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[621, 619])).
% 1.14/1.39 tff(623,plain,
% 1.14/1.39 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[245])).
% 1.14/1.39 tff(624,plain,
% 1.14/1.39 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[623])).
% 1.14/1.39 tff(625,plain,
% 1.14/1.39 (~(elem!1 = s(s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[211, 624])).
% 1.14/1.39 tff(626,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 1.14/1.39 tff(627,plain,
% 1.14/1.39 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[626])).
% 1.14/1.39 tff(628,plain,
% 1.14/1.39 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[627])).
% 1.14/1.39 tff(629,plain,
% 1.14/1.39 (elem!1 = s(s(s(elem!1)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[92, 628, 98])).
% 1.14/1.39 tff(630,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.39 tff(631,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[630, 629])).
% 1.14/1.39 tff(632,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(633,plain,
% 1.14/1.39 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[632, 625])).
% 1.14/1.39 tff(634,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[633, 622])).
% 1.14/1.39 tff(635,plain,((~(s(s(z)) = s(s(s(s(s(z))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(636,plain,
% 1.14/1.39 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[635, 245])).
% 1.14/1.39 tff(637,plain,
% 1.14/1.39 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[636, 620])).
% 1.14/1.39 tff(638,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.39 tff(639,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(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))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(640,plain,
% 1.14/1.39 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(elem!1))) | (~b(s(elem!1), s(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))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(641,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(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)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[640])).
% 1.14/1.39 tff(642,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(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))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[641, 639])).
% 1.14/1.39 tff(643,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, 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))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(644,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(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)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.14/1.39 tff(645,plain,
% 1.14/1.39 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[644, 337, 600, 638, 599, 598])).
% 1.14/1.39 tff(646,plain,
% 1.14/1.39 (((~![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)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(647,plain,
% 1.14/1.39 ((~![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)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(648,plain,
% 1.14/1.39 ((~![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))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.14/1.39 tff(649,plain,
% 1.14/1.39 ((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))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[648, 43])).
% 1.14/1.39 tff(650,plain,
% 1.14/1.39 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[649, 645, 637])).
% 1.14/1.39 tff(651,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(652,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(653,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.24/1.40 tff(654,plain,
% 1.24/1.40 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[653, 189, 650, 615])).
% 1.24/1.40 tff(655,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[654, 614])).
% 1.24/1.40 tff(656,plain,((~b(s(s(s(s(elem!1)))), z)) | (~(s(z) = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(657,plain,
% 1.24/1.40 (~b(s(s(s(s(elem!1)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[656, 245, 591, 584, 396, 379, 555, 580])).
% 1.24/1.40 tff(658,plain,
% 1.24/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(659,plain,
% 1.24/1.40 (~(s(s(s(s(elem!1)))) = z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[658, 29])).
% 1.24/1.40 tff(660,plain,
% 1.24/1.40 (((~![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))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(661,plain,
% 1.24/1.40 ((~![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))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(662,plain,
% 1.24/1.40 ((~![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)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.24/1.40 tff(663,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[662, 43, 659])).
% 1.24/1.40 tff(664,plain,
% 1.24/1.40 (r(s(s(s(s(elem!1)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[663, 657])).
% 1.24/1.40 tff(665,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(666,plain,
% 1.24/1.40 (((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(667,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[666])).
% 1.24/1.40 tff(668,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[667, 665])).
% 1.24/1.40 tff(669,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(670,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.24/1.40 tff(671,plain,
% 1.24/1.40 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[670, 189, 274, 664])).
% 1.24/1.40 tff(672,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[433])).
% 1.24/1.40 tff(673,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[672])).
% 1.24/1.40 tff(674,plain,
% 1.24/1.40 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[433])).
% 1.24/1.40 tff(675,plain,
% 1.24/1.40 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[674])).
% 1.24/1.40 tff(676,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(677,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(678,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.24/1.40 tff(679,plain,
% 1.24/1.40 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[678, 189, 407, 664])).
% 1.24/1.40 tff(680,plain,
% 1.24/1.40 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[679, 675])).
% 1.24/1.40 tff(681,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(682,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[681])).
% 1.24/1.40 tff(683,plain,
% 1.24/1.40 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[682])).
% 1.24/1.40 tff(684,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(685,plain,
% 1.24/1.40 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[684])).
% 1.24/1.40 tff(686,plain,
% 1.24/1.40 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[591, 685])).
% 1.24/1.40 tff(687,assumption,(s(s(s(s(z)))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.40 tff(688,plain,
% 1.24/1.40 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[431])).
% 1.24/1.40 tff(689,plain,
% 1.24/1.40 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[688, 687])).
% 1.24/1.40 tff(690,plain,
% 1.24/1.40 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[689])).
% 1.24/1.40 tff(691,plain,
% 1.24/1.40 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[430, 121, 690, 98, 688, 687])).
% 1.24/1.40 tff(692,assumption,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.40 tff(693,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[692, 691])).
% 1.24/1.40 tff(694,plain,((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(695,plain,
% 1.24/1.40 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[694, 686, 245])).
% 1.24/1.40 tff(696,plain,
% 1.24/1.40 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[695, 683])).
% 1.24/1.40 tff(697,plain,
% 1.24/1.40 (((~![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))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(698,plain,
% 1.24/1.40 ((~![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))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(699,plain,
% 1.24/1.40 ((~![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)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.24/1.40 tff(700,plain,
% 1.24/1.40 ((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)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[699, 43])).
% 1.24/1.40 tff(701,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[700, 696, 680])).
% 1.24/1.40 tff(702,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[701, 673])).
% 1.24/1.40 tff(703,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(704,plain,
% 1.24/1.40 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~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(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(705,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(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(X1, 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(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[704])).
% 1.24/1.40 tff(706,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(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(X1, 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(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[705, 703])).
% 1.24/1.40 tff(707,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(708,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.24/1.40 tff(709,plain,
% 1.24/1.40 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[708, 337, 365, 580, 493])).
% 1.24/1.40 tff(710,plain,
% 1.24/1.40 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[709, 702])).
% 1.24/1.40 tff(711,plain,
% 1.24/1.40 (((~![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))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(712,plain,
% 1.24/1.40 ((~![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))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(713,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.24/1.40 tff(714,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[713, 43])).
% 1.24/1.40 tff(715,plain,
% 1.24/1.40 (s(s(s(s(elem!1)))) = elem!1),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[714, 710, 671])).
% 1.24/1.40 tff(716,plain,
% 1.24/1.40 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[715])).
% 1.24/1.40 tff(717,plain,
% 1.24/1.40 (s(z) = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[245, 716])).
% 1.24/1.40 tff(718,plain,
% 1.24/1.40 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[717])).
% 1.24/1.40 tff(719,plain,
% 1.24/1.40 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.24/1.40 inference(symmetry,[status(thm)],[718])).
% 1.24/1.40 tff(720,plain,
% 1.24/1.40 (s(s(s(elem!1))) = z),
% 1.24/1.40 inference(transitivity,[status(thm)],[130, 719, 14])).
% 1.24/1.40 tff(721,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[133, 720])).
% 1.24/1.40 tff(722,plain,((~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(723,plain,
% 1.24/1.40 (~(s(z) = elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[722, 370, 274, 172, 215, 273, 365, 413, 422, 50])).
% 1.24/1.40 tff(724,plain,
% 1.24/1.40 (((~![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))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(725,plain,
% 1.24/1.40 ((~![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))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(726,plain,
% 1.24/1.40 ((~![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)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[725, 724])).
% 1.24/1.40 tff(727,plain,
% 1.24/1.40 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[726, 43])).
% 1.24/1.40 tff(728,plain,
% 1.24/1.40 (b(s(z), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[727, 723, 417])).
% 1.24/1.40 tff(729,plain,
% 1.24/1.40 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[119])).
% 1.24/1.40 tff(730,plain,
% 1.24/1.40 (~(elem!1 = s(z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[723, 729])).
% 1.24/1.40 tff(731,plain,
% 1.24/1.40 (b(elem!1, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[322, 730, 318])).
% 1.24/1.40 tff(732,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(733,plain,
% 1.24/1.40 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~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(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(734,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~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(X1, 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(elem!1, s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[733])).
% 1.24/1.40 tff(735,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~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(X1, 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(elem!1, s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[734, 732])).
% 1.24/1.40 tff(736,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(737,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.24/1.40 tff(738,plain,
% 1.24/1.40 (~b(elem!1, s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[737, 337, 731, 728, 413])).
% 1.24/1.40 tff(739,plain,
% 1.24/1.40 (~r(elem!1, s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[291, 215, 274])).
% 1.24/1.40 tff(740,plain,
% 1.24/1.40 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[295, 43, 739])).
% 1.24/1.40 tff(741,plain,
% 1.24/1.40 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[740, 738])).
% 1.24/1.40 tff(742,plain,
% 1.24/1.40 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[741])).
% 1.24/1.40 tff(743,plain,
% 1.24/1.40 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.24/1.40 inference(symmetry,[status(thm)],[742])).
% 1.24/1.40 tff(744,plain,
% 1.24/1.40 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[743])).
% 1.24/1.40 tff(745,plain,
% 1.24/1.40 (b(s(elem!1), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.40 inference(symmetry,[status(thm)],[744])).
% 1.24/1.40 tff(746,plain,
% 1.24/1.40 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[358, 352, 273])).
% 1.24/1.40 tff(747,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(748,plain,
% 1.24/1.40 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(749,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[748])).
% 1.24/1.40 tff(750,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[749, 747])).
% 1.24/1.40 tff(751,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(752,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[751, 750])).
% 1.24/1.40 tff(753,plain,
% 1.24/1.40 (~r(z, s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[752, 189, 370, 352])).
% 1.24/1.40 tff(754,plain,
% 1.24/1.40 (b(z, s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[146, 753])).
% 1.24/1.40 tff(755,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(756,plain,
% 1.24/1.40 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(757,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[756])).
% 1.24/1.40 tff(758,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[757, 755])).
% 1.24/1.40 tff(759,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(760,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[759, 758])).
% 1.24/1.41 tff(761,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[760, 337, 365, 396, 754, 379])).
% 1.24/1.41 tff(762,plain,((~r(z, elem!1)) | (~b(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,[]))).
% 1.24/1.41 tff(763,plain,
% 1.24/1.41 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[762, 352, 370, 273])).
% 1.24/1.41 tff(764,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[363, 763, 746, 172])).
% 1.24/1.41 tff(765,plain,((~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(766,plain,
% 1.24/1.41 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[765, 370, 273, 172])).
% 1.24/1.41 tff(767,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(768,plain,
% 1.24/1.41 (((~b(elem!1, s(z))) | (~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(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(769,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[768])).
% 1.24/1.41 tff(770,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[769, 767])).
% 1.24/1.41 tff(771,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(772,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[771, 770])).
% 1.24/1.41 tff(773,plain,
% 1.24/1.41 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[772, 337, 731, 728, 413])).
% 1.24/1.41 tff(774,plain,
% 1.24/1.41 (s(s(s(elem!1))) = elem!1),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[350, 773, 766])).
% 1.24/1.41 tff(775,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.24/1.41 tff(776,plain,
% 1.24/1.41 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[775])).
% 1.24/1.41 tff(777,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.24/1.41 tff(778,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(779,plain,
% 1.24/1.41 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(780,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[779])).
% 1.24/1.41 tff(781,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[780, 778])).
% 1.24/1.41 tff(782,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(783,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.24/1.41 tff(784,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[783, 189, 370, 777, 173])).
% 1.24/1.41 tff(785,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(786,plain,
% 1.24/1.41 (~r(elem!1, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[785, 173, 370])).
% 1.24/1.41 tff(787,plain,
% 1.24/1.41 (b(elem!1, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[322, 786, 247])).
% 1.24/1.41 tff(788,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.24/1.41 tff(789,plain,
% 1.24/1.41 (~r(s(elem!1), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[374, 273, 370])).
% 1.24/1.41 tff(790,plain,
% 1.24/1.41 (b(s(elem!1), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[378, 43, 114, 789])).
% 1.24/1.41 tff(791,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.24/1.41 tff(792,plain,
% 1.24/1.41 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[157, 776])).
% 1.24/1.41 tff(793,plain,
% 1.24/1.41 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[792])).
% 1.24/1.41 tff(794,plain,
% 1.24/1.41 (s(s(s(z))) = s(s(elem!1))),
% 1.24/1.41 inference(transitivity,[status(thm)],[162, 793, 87])).
% 1.24/1.41 tff(795,plain,
% 1.24/1.41 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[794])).
% 1.24/1.41 tff(796,plain,
% 1.24/1.41 (s(s(z)) = s(elem!1)),
% 1.24/1.41 inference(transitivity,[status(thm)],[21, 795, 110])).
% 1.24/1.41 tff(797,plain,
% 1.24/1.41 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[796])).
% 1.24/1.41 tff(798,plain,
% 1.24/1.41 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[797])).
% 1.24/1.41 tff(799,plain,
% 1.24/1.41 (elem!1 = s(z)),
% 1.24/1.41 inference(transitivity,[status(thm)],[92, 798, 104])).
% 1.24/1.41 tff(800,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[247, 799])).
% 1.24/1.41 tff(801,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(802,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[801, 775, 247])).
% 1.24/1.41 tff(803,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.41 tff(804,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.24/1.41 tff(805,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.41 inference(monotonicity,[status(thm)],[804])).
% 1.24/1.41 tff(806,plain,
% 1.24/1.41 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(symmetry,[status(thm)],[805])).
% 1.24/1.41 tff(807,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[273, 806])).
% 1.24/1.41 tff(808,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[803, 807])).
% 1.24/1.41 tff(809,plain,((~(s(s(s(s(z)))) = s(elem!1))) | r(s(s(s(s(z)))), elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(810,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[809, 803, 273])).
% 1.24/1.41 tff(811,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.41 tff(812,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(813,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(814,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[813, 812])).
% 1.24/1.41 tff(815,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[814, 189, 173, 811])).
% 1.24/1.41 tff(816,plain,
% 1.24/1.41 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(817,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[816, 29])).
% 1.24/1.41 tff(818,plain,
% 1.24/1.41 (((~![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))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(819,plain,
% 1.24/1.41 ((~![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))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(820,plain,
% 1.24/1.41 ((~![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)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[819, 818])).
% 1.24/1.41 tff(821,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[820, 43, 817, 815])).
% 1.24/1.41 tff(822,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(823,plain,
% 1.24/1.41 (((~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(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(824,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[823])).
% 1.24/1.41 tff(825,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[824, 822])).
% 1.24/1.41 tff(826,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(elem!1))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(827,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.24/1.41 tff(828,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[827, 189, 788, 811])).
% 1.24/1.41 tff(829,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 1.24/1.41 tff(830,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(831,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(832,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.24/1.41 tff(833,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[832, 43, 829, 828])).
% 1.24/1.41 tff(834,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(835,plain,
% 1.24/1.41 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(836,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[835])).
% 1.24/1.41 tff(837,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[836, 834])).
% 1.24/1.41 tff(838,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(839,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.24/1.41 tff(840,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[839, 337, 600, 599, 833, 821])).
% 1.24/1.41 tff(841,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(842,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[841, 810, 599, 600, 173, 788])).
% 1.24/1.41 tff(843,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(844,plain,
% 1.24/1.41 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[843])).
% 1.24/1.41 tff(845,plain,
% 1.24/1.41 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[844])).
% 1.24/1.41 tff(846,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[516, 845])).
% 1.24/1.41 tff(847,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(848,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(849,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.24/1.41 tff(850,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[849, 43])).
% 1.24/1.41 tff(851,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[850, 846])).
% 1.24/1.41 tff(852,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[851, 842])).
% 1.24/1.41 tff(853,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.24/1.41 tff(854,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(855,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(856,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[855, 854])).
% 1.24/1.41 tff(857,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[856, 43])).
% 1.24/1.41 tff(858,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[857, 803, 853])).
% 1.24/1.41 tff(859,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(860,plain,
% 1.24/1.41 (((~b(s(z), elem!1)) | (~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(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))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(861,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X1, 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(s(s(s(z)))), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[860])).
% 1.24/1.42 tff(862,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X1, 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(s(s(s(z)))), s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[861, 859])).
% 1.24/1.42 tff(863,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(864,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.24/1.42 tff(865,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[864, 337, 327, 791, 858, 852])).
% 1.24/1.42 tff(866,plain,(r(s(s(s(s(z)))), elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(867,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[866, 802, 791, 790, 396, 173, 788, 787, 273])).
% 1.24/1.42 tff(868,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(869,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(870,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.24/1.42 tff(871,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[870, 189, 370, 867])).
% 1.24/1.42 tff(872,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[820, 43, 817, 871])).
% 1.24/1.42 tff(873,plain,
% 1.24/1.42 (((~b(s(elem!1), z)) | (~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(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(874,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[873])).
% 1.24/1.42 tff(875,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[874, 834])).
% 1.24/1.42 tff(876,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(877,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[876, 875])).
% 1.24/1.42 tff(878,plain,
% 1.24/1.42 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[877, 337, 396, 790, 872])).
% 1.24/1.42 tff(879,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(880,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(881,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[880, 879])).
% 1.24/1.42 tff(882,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[881, 189, 273, 867])).
% 1.24/1.42 tff(883,plain,
% 1.24/1.42 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[832, 43, 882])).
% 1.24/1.42 tff(884,plain,
% 1.24/1.42 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[883, 878])).
% 1.24/1.42 tff(885,plain,
% 1.24/1.42 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[884])).
% 1.24/1.42 tff(886,plain,
% 1.24/1.42 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[162, 885, 91, 776])).
% 1.24/1.42 tff(887,plain,
% 1.24/1.42 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[886])).
% 1.24/1.42 tff(888,plain,
% 1.24/1.42 (s(s(z)) = s(s(elem!1))),
% 1.24/1.42 inference(transitivity,[status(thm)],[21, 887, 87])).
% 1.24/1.42 tff(889,plain,
% 1.24/1.42 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[888])).
% 1.24/1.42 tff(890,plain,
% 1.24/1.42 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.24/1.42 inference(symmetry,[status(thm)],[889])).
% 1.24/1.42 tff(891,plain,
% 1.24/1.42 (s(elem!1) = s(z)),
% 1.24/1.42 inference(transitivity,[status(thm)],[111, 890, 104])).
% 1.24/1.42 tff(892,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[50, 891])).
% 1.24/1.42 tff(893,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(894,plain,
% 1.24/1.42 (~r(s(elem!1), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[893, 774, 273, 370, 50, 173, 728, 730])).
% 1.24/1.42 tff(895,plain,
% 1.24/1.42 (((~![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)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(896,plain,
% 1.24/1.42 ((~![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)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(897,plain,
% 1.24/1.42 ((~![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))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.24/1.42 tff(898,plain,
% 1.24/1.42 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[897, 43])).
% 1.24/1.42 tff(899,plain,
% 1.24/1.42 (b(s(elem!1), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[898, 894, 50])).
% 1.24/1.42 tff(900,plain,
% 1.24/1.42 (b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[899, 745])).
% 1.24/1.42 tff(901,plain,
% 1.24/1.42 (s(s(s(elem!1))) = elem!1),
% 1.24/1.42 inference(symmetry,[status(thm)],[741])).
% 1.24/1.42 tff(902,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[901])).
% 1.24/1.42 tff(903,plain,
% 1.24/1.42 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[902])).
% 1.24/1.42 tff(904,plain,
% 1.24/1.42 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[741, 743])).
% 1.24/1.42 tff(905,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[904])).
% 1.24/1.42 tff(906,plain,
% 1.24/1.42 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[365, 905])).
% 1.24/1.42 tff(907,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[906, 903])).
% 1.24/1.42 tff(908,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(909,plain,
% 1.24/1.42 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(910,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[909])).
% 1.24/1.42 tff(911,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[910, 908])).
% 1.24/1.42 tff(912,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(913,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.24/1.42 tff(914,plain,
% 1.24/1.42 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[913, 337, 422, 413])).
% 1.24/1.42 tff(915,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[914, 907, 900])).
% 1.24/1.42 tff(916,plain,((~r(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(917,plain,
% 1.24/1.42 (~r(z, elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[916, 365, 50, 273, 81, 274, 172, 147, 275])).
% 1.24/1.42 tff(918,plain,
% 1.24/1.42 (((~![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))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(919,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(920,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[919, 918])).
% 1.24/1.42 tff(921,plain,
% 1.24/1.42 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[920, 43])).
% 1.24/1.42 tff(922,plain,
% 1.24/1.42 (b(z, elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[921, 917, 61])).
% 1.24/1.42 tff(923,plain,
% 1.24/1.42 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 1.24/1.42 inference(monotonicity,[status(thm)],[775])).
% 1.24/1.42 tff(924,plain,
% 1.24/1.42 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[923])).
% 1.24/1.42 tff(925,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.24/1.42 tff(926,plain,
% 1.24/1.42 (b(z, s(s(s(elem!1))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.24/1.42 tff(927,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[82, 926])).
% 1.24/1.42 tff(928,plain,((~(s(s(s(elem!1))) = elem!1)) | b(z, s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(929,plain,
% 1.24/1.42 (~(s(s(s(elem!1))) = elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[928, 922, 82])).
% 1.24/1.42 tff(930,plain,
% 1.24/1.42 (b(z, elem!1) <=> b(z, s(z))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[230])).
% 1.24/1.42 tff(931,plain,
% 1.24/1.42 (b(z, s(z)) <=> b(z, elem!1)),
% 1.24/1.42 inference(symmetry,[status(thm)],[930])).
% 1.24/1.42 tff(932,plain,
% 1.24/1.42 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[931])).
% 1.24/1.42 tff(933,plain,
% 1.24/1.42 (~b(z, elem!1)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[69, 932])).
% 1.24/1.42 tff(934,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[925, 933])).
% 1.24/1.42 tff(935,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(936,plain,
% 1.24/1.42 (~(elem!1 = s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[935, 922, 69])).
% 1.24/1.42 tff(937,plain,
% 1.24/1.42 (b(elem!1, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[322, 936, 318])).
% 1.24/1.42 tff(938,plain,
% 1.24/1.42 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[258])).
% 1.24/1.42 tff(939,plain,
% 1.24/1.42 (~(elem!1 = s(s(s(elem!1))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[929, 938])).
% 1.24/1.42 tff(940,plain,
% 1.24/1.42 (b(elem!1, s(s(s(elem!1))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[296, 939])).
% 1.24/1.42 tff(941,plain,
% 1.24/1.42 (~b(s(z), s(s(s(elem!1))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[345, 327, 326, 325])).
% 1.24/1.42 tff(942,plain,
% 1.24/1.42 (r(s(z), s(s(s(elem!1))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[310, 43, 211, 941])).
% 1.24/1.42 tff(943,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(944,plain,
% 1.24/1.42 (((~b(s(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(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, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(945,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[944])).
% 1.24/1.42 tff(946,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[945, 943])).
% 1.24/1.42 tff(947,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(948,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.24/1.42 tff(949,plain,
% 1.24/1.42 (~b(z, s(s(s(elem!1))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[948, 337, 925, 326, 325])).
% 1.24/1.42 tff(950,plain,
% 1.24/1.42 (r(z, s(s(s(elem!1))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[146, 949])).
% 1.24/1.42 tff(951,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(952,plain,
% 1.24/1.42 (((~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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(953,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[952])).
% 1.24/1.42 tff(954,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[953, 951])).
% 1.24/1.42 tff(955,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(956,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.24/1.42 tff(957,plain,
% 1.24/1.42 (~r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[956, 189, 950, 942])).
% 1.24/1.42 tff(958,plain,
% 1.24/1.42 (b(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[80, 957])).
% 1.24/1.42 tff(959,plain,
% 1.24/1.42 (~r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[304, 189, 950, 942])).
% 1.24/1.42 tff(960,plain,
% 1.24/1.42 (((~![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))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(961,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(962,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[961, 960])).
% 1.24/1.42 tff(963,plain,
% 1.24/1.42 (b(s(z), z) | r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[962, 43, 74])).
% 1.24/1.42 tff(964,plain,
% 1.24/1.42 (b(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[963, 959])).
% 1.24/1.42 tff(965,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(966,plain,
% 1.24/1.42 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(967,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[966])).
% 1.24/1.42 tff(968,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[967, 965])).
% 1.24/1.42 tff(969,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(970,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.24/1.42 tff(971,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[970, 337, 925, 327, 964, 958])).
% 1.24/1.42 tff(972,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(973,plain,
% 1.24/1.42 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[972, 940, 922, 937])).
% 1.24/1.42 tff(974,plain,
% 1.24/1.42 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[350, 973, 929])).
% 1.24/1.43 tff(975,plain,
% 1.24/1.43 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.24/1.43 inference(commutativity,[status(thm)],[])).
% 1.24/1.43 tff(976,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.24/1.43 tff(977,plain,
% 1.24/1.43 (s(elem!1) = elem!1),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[976, 975])).
% 1.24/1.43 tff(978,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.24/1.43 tff(979,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[978, 977])).
% 1.24/1.43 tff(980,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(981,plain,
% 1.24/1.43 (~(elem!1 = s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[980, 265])).
% 1.24/1.43 tff(982,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(983,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.43 tff(984,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.24/1.43 tff(985,plain,
% 1.24/1.43 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[350, 276, 984])).
% 1.24/1.43 tff(986,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(987,plain,
% 1.24/1.43 (((~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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(988,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[987])).
% 1.24/1.43 tff(989,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[988, 986])).
% 1.24/1.43 tff(990,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(991,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.24/1.43 tff(992,plain,
% 1.24/1.43 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[991, 189, 273, 985])).
% 1.24/1.43 tff(993,plain,
% 1.24/1.43 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[579, 992, 983])).
% 1.24/1.43 tff(994,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(995,plain,
% 1.24/1.43 (((~b(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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(996,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[995])).
% 1.24/1.43 tff(997,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[996, 994])).
% 1.24/1.43 tff(998,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(999,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.24/1.43 tff(1000,plain,
% 1.24/1.43 (~b(elem!1, s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[999, 337, 365, 993, 982])).
% 1.24/1.43 tff(1001,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.43 tff(1002,plain,
% 1.24/1.43 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[295, 43, 1001])).
% 1.24/1.43 tff(1003,plain,
% 1.24/1.43 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1002, 1000])).
% 1.24/1.43 tff(1004,plain,
% 1.24/1.43 (s(s(s(elem!1))) = elem!1),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1003, 277])).
% 1.24/1.43 tff(1005,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[276, 1004])).
% 1.24/1.43 tff(1006,plain,((s(s(s(elem!1))) = elem!1) | r(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1007,plain,
% 1.24/1.43 (~b(elem!1, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1006, 973, 365, 929, 428, 273, 292])).
% 1.24/1.43 tff(1008,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(1009,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(1010,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(1011,plain,
% 1.24/1.43 (((~![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)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1012,plain,
% 1.24/1.43 ((~![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)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1013,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.24/1.43 tff(1014,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1013, 43, 1010, 1009, 1008])).
% 1.24/1.43 tff(1015,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1016,plain,
% 1.24/1.43 (r(elem!1, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1015, 1007, 981])).
% 1.24/1.43 tff(1017,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1018,plain,
% 1.24/1.43 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1019,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1018])).
% 1.24/1.43 tff(1020,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1019, 1017])).
% 1.24/1.43 tff(1021,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1022,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.24/1.43 tff(1023,plain,
% 1.24/1.43 ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1022, 189])).
% 1.24/1.43 tff(1024,plain,
% 1.24/1.43 (~r(s(elem!1), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1023, 1016, 274])).
% 1.24/1.43 tff(1025,plain,
% 1.24/1.43 (b(s(elem!1), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[378, 43, 114, 1024])).
% 1.24/1.43 tff(1026,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1027,plain,
% 1.24/1.43 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1028,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1027])).
% 1.24/1.43 tff(1029,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1028, 1026])).
% 1.24/1.43 tff(1030,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1031,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 1.24/1.43 tff(1032,plain,
% 1.24/1.43 ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1031, 189])).
% 1.24/1.43 tff(1033,plain,
% 1.24/1.43 (~r(z, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1032, 1016, 274])).
% 1.24/1.43 tff(1034,plain,
% 1.24/1.43 (b(z, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[395, 1033])).
% 1.24/1.43 tff(1035,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1036,plain,
% 1.24/1.43 (((~b(z, elem!1)) | (~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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1037,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1036])).
% 1.24/1.43 tff(1038,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1037, 1035])).
% 1.24/1.43 tff(1039,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1040,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 1.24/1.43 tff(1041,plain,
% 1.24/1.43 (~b(s(s(s(elem!1))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1040, 337, 922, 365, 1034, 1025])).
% 1.24/1.43 tff(1042,plain,
% 1.24/1.43 (r(s(s(s(elem!1))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[406, 43, 133, 1041])).
% 1.24/1.43 tff(1043,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1044,plain,
% 1.24/1.43 (((~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(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1045,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1044])).
% 1.24/1.43 tff(1046,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1045, 1043])).
% 1.24/1.43 tff(1047,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1048,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 1.24/1.43 tff(1049,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1048, 189, 274, 1042, 974])).
% 1.24/1.43 tff(1050,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | b(z, s(z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1051,plain,
% 1.24/1.43 (b(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1050, 364, 273, 82, 274, 50, 172, 275])).
% 1.24/1.43 tff(1052,plain,
% 1.24/1.43 (b(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[727, 272, 417])).
% 1.24/1.43 tff(1053,plain,
% 1.24/1.43 (~r(z, elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[765, 351, 273, 172])).
% 1.24/1.43 tff(1054,plain,
% 1.24/1.43 (b(z, elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[921, 1053, 61])).
% 1.24/1.43 tff(1055,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1056,plain,
% 1.24/1.43 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1057,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1056])).
% 1.24/1.43 tff(1058,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1057, 1055])).
% 1.24/1.43 tff(1059,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1060,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 1.24/1.43 tff(1061,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1060, 337, 1054, 323, 1052, 1051])).
% 1.24/1.43 tff(1062,plain,((elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1063,plain,
% 1.24/1.43 (elem!1 = s(z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1062, 276, 82, 274, 50, 172, 275, 273])).
% 1.24/1.43 tff(1064,plain,
% 1.24/1.43 (s(elem!1) = s(s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1063])).
% 1.24/1.43 tff(1065,plain,
% 1.24/1.43 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1064])).
% 1.24/1.43 tff(1066,plain,
% 1.24/1.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1065])).
% 1.24/1.43 tff(1067,plain,
% 1.24/1.43 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1066])).
% 1.24/1.43 tff(1068,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[147, 1067])).
% 1.24/1.43 tff(1069,plain,
% 1.24/1.43 (s(s(z)) = s(elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[1064])).
% 1.24/1.43 tff(1070,plain,
% 1.24/1.43 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1069])).
% 1.24/1.43 tff(1071,plain,
% 1.24/1.43 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.24/1.43 inference(symmetry,[status(thm)],[1070])).
% 1.24/1.43 tff(1072,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1066])).
% 1.24/1.43 tff(1073,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1063])).
% 1.24/1.43 tff(1074,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1073, 1072])).
% 1.24/1.43 tff(1075,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.24/1.43 tff(1076,plain,
% 1.24/1.43 (b(elem!1, s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[740, 282])).
% 1.24/1.43 tff(1077,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(1078,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1079,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1080,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.24/1.43 tff(1081,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1080, 189, 353, 1077, 215])).
% 1.24/1.43 tff(1082,plain,((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1083,plain,
% 1.24/1.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1082, 1077, 215])).
% 1.24/1.43 tff(1084,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[363, 1083, 172])).
% 1.24/1.43 tff(1085,plain,
% 1.24/1.43 (~r(elem!1, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1032, 1077, 274])).
% 1.24/1.43 tff(1086,plain,
% 1.24/1.43 (b(elem!1, s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1015, 1085, 981])).
% 1.24/1.43 tff(1087,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1006, 1086, 1084, 276, 428, 273, 739])).
% 1.24/1.43 tff(1088,plain,
% 1.24/1.43 (~b(elem!1, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[345, 1087, 324, 1076])).
% 1.24/1.43 tff(1089,plain,
% 1.24/1.43 (elem!1 = s(z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[322, 1088, 1075])).
% 1.24/1.43 tff(1090,plain,
% 1.24/1.43 (s(elem!1) = s(s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1089])).
% 1.24/1.43 tff(1091,plain,
% 1.24/1.43 (s(s(z)) = s(elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[1090])).
% 1.24/1.43 tff(1092,plain,
% 1.24/1.43 (s(z) = elem!1),
% 1.24/1.43 inference(symmetry,[status(thm)],[1089])).
% 1.24/1.43 tff(1093,plain,
% 1.24/1.43 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1092, 1091])).
% 1.24/1.43 tff(1094,plain,
% 1.24/1.43 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1093])).
% 1.24/1.43 tff(1095,plain,
% 1.24/1.43 (b(s(z), s(s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1086, 1094])).
% 1.24/1.43 tff(1096,plain,
% 1.24/1.43 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1090])).
% 1.24/1.43 tff(1097,plain,
% 1.24/1.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1096])).
% 1.24/1.43 tff(1098,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1097, 1090])).
% 1.24/1.43 tff(1099,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1084, 1098])).
% 1.24/1.43 tff(1100,plain,
% 1.24/1.43 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1097])).
% 1.24/1.43 tff(1101,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[215, 1100])).
% 1.24/1.43 tff(1102,plain,
% 1.24/1.43 (s(s(z)) = s(elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[231])).
% 1.24/1.43 tff(1103,plain,
% 1.24/1.43 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1102])).
% 1.24/1.43 tff(1104,plain,
% 1.24/1.43 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1103])).
% 1.24/1.43 tff(1105,plain,
% 1.24/1.43 (r(z, s(s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1077, 1104])).
% 1.24/1.43 tff(1106,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 1.24/1.43 tff(1107,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1106, 1105])).
% 1.24/1.43 tff(1108,plain,(r(z, s(s(z))) | (~r(z, s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1109,plain,
% 1.24/1.43 (r(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1108, 1089, 1077])).
% 1.24/1.43 tff(1110,plain,
% 1.24/1.43 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[233])).
% 1.24/1.43 tff(1111,plain,
% 1.24/1.43 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1102, 1110])).
% 1.24/1.43 tff(1112,plain,
% 1.24/1.43 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1111])).
% 1.24/1.43 tff(1113,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.43 tff(1114,plain,
% 1.24/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.24/1.43 tff(1115,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.43 tff(1116,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.24/1.43 tff(1117,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1118,plain,
% 1.24/1.44 (((~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)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1119,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1118])).
% 1.24/1.44 tff(1120,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1119, 1117])).
% 1.24/1.44 tff(1121,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1122,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.24/1.44 tff(1123,plain,
% 1.24/1.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1122, 189, 1116, 1115])).
% 1.24/1.44 tff(1124,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1123, 1114])).
% 1.24/1.44 tff(1125,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1126,plain,
% 1.24/1.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1125, 1089, 1109, 1101])).
% 1.24/1.44 tff(1127,plain,
% 1.24/1.44 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[579, 1126, 428])).
% 1.24/1.44 tff(1128,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1102, 1110])).
% 1.24/1.44 tff(1129,plain,
% 1.24/1.44 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1128])).
% 1.24/1.44 tff(1130,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[638, 1129])).
% 1.24/1.44 tff(1131,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(1132,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1131, 1130])).
% 1.24/1.44 tff(1133,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1134,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1133, 1127, 1089])).
% 1.24/1.44 tff(1135,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1097])).
% 1.24/1.44 tff(1136,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1089])).
% 1.24/1.44 tff(1137,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1087, 1136])).
% 1.24/1.44 tff(1138,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1137, 1135])).
% 1.24/1.44 tff(1139,plain,
% 1.24/1.44 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[230, 233])).
% 1.24/1.44 tff(1140,plain,
% 1.24/1.44 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1139])).
% 1.24/1.44 tff(1141,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(1142,plain,
% 1.24/1.44 (r(elem!1, s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.24/1.44 tff(1143,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1001, 1142])).
% 1.24/1.44 tff(1144,plain,((~r(s(z), s(s(s(s(z)))))) | r(elem!1, s(s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1145,plain,
% 1.24/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1144, 1089, 739])).
% 1.24/1.44 tff(1146,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1147,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1148,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.24/1.44 tff(1149,plain,
% 1.24/1.44 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1148, 43])).
% 1.24/1.44 tff(1150,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1149, 516])).
% 1.24/1.44 tff(1151,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1150, 1145])).
% 1.24/1.44 tff(1152,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1153,plain,
% 1.24/1.44 (((~b(s(s(s(s(z)))), 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)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1154,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(X1, 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(s(s(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)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1153])).
% 1.24/1.44 tff(1155,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(X1, 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(s(s(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))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1154, 1152])).
% 1.24/1.44 tff(1156,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1157,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.24/1.44 tff(1158,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1157, 337, 1151, 1138, 1134, 1099, 1095])).
% 1.24/1.44 tff(1159,plain,((~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | r(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1160,plain,
% 1.24/1.44 (~r(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1159, 276, 318, 311, 147, 273, 172, 274])).
% 1.24/1.44 tff(1161,plain,
% 1.24/1.44 (b(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[395, 1160])).
% 1.24/1.44 tff(1162,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[230])).
% 1.24/1.44 tff(1163,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[1162])).
% 1.24/1.44 tff(1164,plain,
% 1.24/1.44 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[233])).
% 1.24/1.44 tff(1165,plain,
% 1.24/1.44 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[230])).
% 1.24/1.44 tff(1166,plain,
% 1.24/1.44 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(transitivity,[status(thm)],[1165, 1164, 1163])).
% 1.24/1.44 tff(1167,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[352, 1166])).
% 1.24/1.44 tff(1168,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.44 tff(1169,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(1170,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1171,plain,
% 1.24/1.44 (((~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)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1172,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1171])).
% 1.24/1.44 tff(1173,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1172, 1170])).
% 1.24/1.44 tff(1174,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1175,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 1.24/1.44 tff(1176,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1175, 189, 274, 1169, 1168])).
% 1.24/1.44 tff(1177,plain,((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1178,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1177, 1167, 274])).
% 1.24/1.44 tff(1179,plain,
% 1.24/1.44 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1102])).
% 1.24/1.44 tff(1180,plain,
% 1.24/1.44 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1179])).
% 1.24/1.44 tff(1181,plain,
% 1.24/1.44 (b(z, s(s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[600, 1180])).
% 1.24/1.44 tff(1182,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[233, 231])).
% 1.24/1.44 tff(1183,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[363, 746, 172])).
% 1.24/1.44 tff(1184,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.24/1.44 tff(1185,plain,
% 1.24/1.44 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1111])).
% 1.24/1.44 tff(1186,plain,
% 1.24/1.44 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1102])).
% 1.24/1.44 tff(1187,plain,
% 1.24/1.44 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1186])).
% 1.24/1.44 tff(1188,plain,
% 1.24/1.44 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[230])).
% 1.24/1.44 tff(1189,plain,
% 1.24/1.44 (r(s(elem!1), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[273, 1188])).
% 1.24/1.44 tff(1190,plain,
% 1.24/1.44 (r(s(s(z)), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1189, 1187])).
% 1.24/1.44 tff(1191,plain,
% 1.24/1.44 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1165, 1164])).
% 1.24/1.44 tff(1192,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[352, 1191])).
% 1.24/1.44 tff(1193,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1194,plain,
% 1.24/1.44 (((~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(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1195,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1194])).
% 1.24/1.44 tff(1196,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1195, 1193])).
% 1.24/1.44 tff(1197,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1198,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 1.24/1.44 tff(1199,plain,
% 1.24/1.44 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1198, 189, 1192])).
% 1.24/1.44 tff(1200,plain,
% 1.24/1.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1199, 1190])).
% 1.24/1.44 tff(1201,plain,
% 1.24/1.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1200, 1185])).
% 1.24/1.44 tff(1202,plain,
% 1.24/1.44 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[579, 1201, 428])).
% 1.24/1.44 tff(1203,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1133, 1202, 230])).
% 1.24/1.44 tff(1204,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1205,plain,
% 1.24/1.44 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(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(s(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1206,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))), z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1205])).
% 1.24/1.44 tff(1207,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z)))), z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1206, 1204])).
% 1.24/1.44 tff(1208,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1209,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.24/1.44 tff(1210,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1209, 337, 1203, 1184, 1181])).
% 1.24/1.44 tff(1211,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[820, 43, 817, 1210, 1178])).
% 1.24/1.44 tff(1212,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~(elem!1 = s(z))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1213,plain,
% 1.24/1.44 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1212, 1161, 1063, 274, 172, 273])).
% 1.24/1.44 tff(1214,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[350, 1213, 276])).
% 1.24/1.44 tff(1215,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1214, 1074])).
% 1.24/1.44 tff(1216,plain,
% 1.24/1.44 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[230, 231])).
% 1.24/1.44 tff(1217,plain,
% 1.24/1.44 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1216])).
% 1.24/1.44 tff(1218,plain,
% 1.24/1.44 ((~b(s(z), s(s(z)))) <=> (~b(elem!1, s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1217])).
% 1.24/1.44 tff(1219,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.24/1.44 tff(1220,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1221,plain,
% 1.24/1.44 (((~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(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1222,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1221])).
% 1.24/1.44 tff(1223,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.24/1.44 tff(1224,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1225,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.24/1.44 tff(1226,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1225, 189, 1219, 215, 1113])).
% 1.24/1.44 tff(1227,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1228,plain,
% 1.24/1.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1227, 1219, 215])).
% 1.24/1.44 tff(1229,plain,
% 1.24/1.44 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[579, 1228, 983])).
% 1.24/1.44 tff(1230,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1133, 1229, 230])).
% 1.24/1.44 tff(1231,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.44 tff(1232,plain,
% 1.24/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1144, 230, 739])).
% 1.24/1.44 tff(1233,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1150, 1232])).
% 1.24/1.44 tff(1234,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1235,plain,
% 1.24/1.44 (((~b(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(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(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(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1236,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1235])).
% 1.24/1.45 tff(1237,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.24/1.45 tff(1238,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1239,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.24/1.45 tff(1240,plain,
% 1.24/1.45 (~b(s(z), s(s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1239, 337, 1233, 1231, 1230])).
% 1.24/1.45 tff(1241,plain,
% 1.24/1.45 (~b(elem!1, s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1240, 1218])).
% 1.24/1.45 tff(1242,plain,
% 1.24/1.45 (~r(elem!1, s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1023, 1219, 274])).
% 1.24/1.45 tff(1243,plain,
% 1.24/1.45 (b(elem!1, s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1015, 1242, 1008])).
% 1.24/1.45 tff(1244,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1243, 1241])).
% 1.24/1.45 tff(1245,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1246,plain,
% 1.24/1.45 (~r(s(elem!1), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1245, 1063, 1215, 981, 428, 274, 147])).
% 1.24/1.45 tff(1247,plain,
% 1.24/1.45 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1102])).
% 1.24/1.45 tff(1248,plain,
% 1.24/1.45 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.24/1.45 inference(symmetry,[status(thm)],[1247])).
% 1.24/1.45 tff(1249,plain,
% 1.24/1.45 ((~b(s(elem!1), z)) <=> (~b(s(s(z)), z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1248])).
% 1.24/1.45 tff(1250,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.24/1.45 tff(1251,plain,
% 1.24/1.45 (~b(s(s(z)), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.24/1.45 tff(1252,plain,
% 1.24/1.45 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1102])).
% 1.24/1.45 tff(1253,plain,
% 1.24/1.45 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.24/1.45 inference(symmetry,[status(thm)],[1252])).
% 1.24/1.45 tff(1254,plain,
% 1.24/1.45 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1253])).
% 1.24/1.45 tff(1255,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.24/1.45 tff(1256,plain,
% 1.24/1.45 (~r(s(s(z)), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.24/1.45 tff(1257,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1258,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1259,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.24/1.45 tff(1260,plain,
% 1.24/1.45 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1259, 43, 31])).
% 1.24/1.45 tff(1261,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1260, 1256, 1251])).
% 1.24/1.45 tff(1262,plain,(r(s(elem!1), z) | (~(elem!1 = s(z))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1263,plain,
% 1.24/1.45 (b(s(elem!1), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1262, 1246, 1063])).
% 1.24/1.45 tff(1264,plain,
% 1.24/1.45 (b(s(s(z)), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1263, 1071])).
% 1.24/1.45 tff(1265,plain,
% 1.24/1.45 (~(s(s(s(z))) = s(s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[452, 1063, 50])).
% 1.24/1.45 tff(1266,plain,
% 1.24/1.45 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1144, 1063, 292])).
% 1.24/1.45 tff(1267,plain,
% 1.24/1.45 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1150, 1266])).
% 1.24/1.45 tff(1268,plain,
% 1.24/1.45 (s(z) = elem!1),
% 1.24/1.45 inference(symmetry,[status(thm)],[230])).
% 1.24/1.45 tff(1269,plain,
% 1.24/1.45 (s(s(s(z))) = s(s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[232])).
% 1.24/1.45 tff(1270,plain,
% 1.24/1.45 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1269, 1268])).
% 1.24/1.45 tff(1271,plain,
% 1.24/1.45 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1270])).
% 1.24/1.45 tff(1272,plain,
% 1.24/1.45 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1271])).
% 1.24/1.45 tff(1273,plain,
% 1.24/1.45 (s(z) = elem!1),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[230, 120])).
% 1.24/1.45 tff(1274,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.24/1.45 tff(1275,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(1276,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1277,plain,
% 1.24/1.45 (((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1278,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1277])).
% 1.24/1.45 tff(1279,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.24/1.45 tff(1280,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1281,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.24/1.45 tff(1282,plain,
% 1.24/1.45 (~b(s(s(s(z))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1281, 337, 1275, 2, 1231])).
% 1.24/1.45 tff(1283,plain,
% 1.24/1.45 (r(s(s(s(z))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[46, 43, 33, 1282])).
% 1.24/1.45 tff(1284,plain,
% 1.24/1.45 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[527])).
% 1.24/1.45 tff(1285,plain,
% 1.24/1.45 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1284])).
% 1.24/1.45 tff(1286,plain,
% 1.24/1.45 (~(s(s(z)) = s(s(s(z))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[458, 1285])).
% 1.24/1.45 tff(1287,plain,
% 1.24/1.45 (r(s(s(z)), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[788, 1187])).
% 1.24/1.45 tff(1288,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1289,plain,
% 1.24/1.45 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1290,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1289])).
% 1.24/1.45 tff(1291,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.24/1.45 tff(1292,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1293,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.24/1.45 tff(1294,plain,
% 1.24/1.45 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1293, 189, 1283])).
% 1.24/1.45 tff(1295,plain,
% 1.24/1.45 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1294, 1287])).
% 1.24/1.45 tff(1296,plain,
% 1.24/1.45 (((~![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)))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1297,plain,
% 1.24/1.45 ((~![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)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1298,plain,
% 1.24/1.45 ((~![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))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.24/1.45 tff(1299,plain,
% 1.24/1.45 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1298, 43, 1295])).
% 1.24/1.45 tff(1300,plain,
% 1.24/1.45 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1299, 1286])).
% 1.24/1.45 tff(1301,assumption,(b(z, s(z))), introduced(assumption)).
% 1.24/1.45 tff(1302,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1303,plain,
% 1.24/1.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(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(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1304,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, 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(X1, 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)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1303])).
% 1.24/1.45 tff(1305,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, 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(X1, 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)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1304, 1302])).
% 1.24/1.45 tff(1306,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1307,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.24/1.45 tff(1308,plain,
% 1.24/1.45 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1307, 337, 1301, 1275, 2, 1274])).
% 1.24/1.45 tff(1309,plain,
% 1.24/1.45 (~b(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1308, 1300])).
% 1.24/1.45 tff(1310,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1311,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1312,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.24/1.45 tff(1313,plain,
% 1.24/1.45 (r(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1312, 43, 178, 1309])).
% 1.24/1.45 tff(1314,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1315,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1316,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.24/1.45 tff(1317,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1316, 189, 275, 1313, 1283])).
% 1.24/1.45 tff(1318,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(s(z))) = s(s(z))) | (~r(s(elem!1), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1319,plain,
% 1.24/1.45 (~b(z, s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1318, 2, 275, 1275, 1274, 458, 1189, 230, 1231])).
% 1.24/1.45 tff(1320,plain,
% 1.24/1.45 (~b(z, elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[935, 1319, 230])).
% 1.24/1.45 tff(1321,plain,
% 1.24/1.45 (r(z, elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[921, 1320, 65])).
% 1.24/1.45 tff(1322,plain,
% 1.24/1.45 (~r(s(s(elem!1)), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[485, 1321, 1273, 273, 458])).
% 1.24/1.45 tff(1323,plain,
% 1.24/1.45 (~r(s(s(s(z))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1322, 1272])).
% 1.24/1.45 tff(1324,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1283, 1323])).
% 1.24/1.45 tff(1325,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = s(s(z))) | (z = elem!1) | (~r(s(z), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1326,plain,
% 1.24/1.45 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1325, 1063, 1267, 1215, 273, 1265, 61, 275, 1264])).
% 1.24/1.45 tff(1327,plain,
% 1.24/1.45 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[548, 1326])).
% 1.24/1.45 tff(1328,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1329,plain,
% 1.24/1.45 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1330,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1329])).
% 1.24/1.45 tff(1331,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.24/1.45 tff(1332,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1333,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.24/1.46 tff(1334,plain,
% 1.24/1.46 (~r(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1333, 189, 1327, 1068])).
% 1.24/1.46 tff(1335,plain,
% 1.24/1.46 (b(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1312, 43, 178, 1334])).
% 1.24/1.46 tff(1336,plain,
% 1.24/1.46 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1069])).
% 1.24/1.46 tff(1337,plain,
% 1.24/1.46 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1336])).
% 1.24/1.46 tff(1338,plain,
% 1.24/1.46 (b(z, s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1161, 1337])).
% 1.24/1.46 tff(1339,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.46 tff(1340,plain,
% 1.24/1.46 (~r(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1333, 189, 1339, 1115])).
% 1.24/1.46 tff(1341,plain,
% 1.24/1.46 (b(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1312, 43, 178, 1340])).
% 1.24/1.46 tff(1342,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.24/1.46 tff(1343,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1344,plain,
% 1.24/1.46 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1345,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1344])).
% 1.24/1.46 tff(1346,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.24/1.46 tff(1347,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1348,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.24/1.46 tff(1349,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1348, 337, 1274, 1342, 1341])).
% 1.24/1.46 tff(1350,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1351,plain,
% 1.24/1.46 (((~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(z)), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1352,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1351])).
% 1.24/1.46 tff(1353,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1352, 1350])).
% 1.24/1.46 tff(1354,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1355,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 1.24/1.46 tff(1356,plain,
% 1.24/1.46 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1355, 189, 1339])).
% 1.24/1.46 tff(1357,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1356, 1114])).
% 1.24/1.46 tff(1358,plain,
% 1.24/1.46 (((~![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))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1359,plain,
% 1.24/1.46 ((~![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))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1360,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.24/1.46 tff(1361,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1360, 43, 458, 1357, 1349])).
% 1.24/1.46 tff(1362,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1363,plain,
% 1.24/1.46 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1362, 1338, 1264, 1327, 1265, 1063, 1068])).
% 1.24/1.46 tff(1364,plain,
% 1.24/1.46 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[579, 1363, 428])).
% 1.24/1.46 tff(1365,plain,
% 1.24/1.46 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1133, 1364, 1063])).
% 1.24/1.46 tff(1366,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1367,plain,
% 1.24/1.46 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1368,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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))), z)) | (~b(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1367])).
% 1.24/1.46 tff(1369,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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))), z)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1368, 1366])).
% 1.24/1.46 tff(1370,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1371,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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))), z)) | (~b(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 1.24/1.46 tff(1372,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1371, 337, 1365, 1264, 1338, 1335])).
% 1.24/1.46 tff(1373,plain,
% 1.24/1.46 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1360, 43, 1265, 1372])).
% 1.24/1.46 tff(1374,plain,
% 1.24/1.46 (s(z) = elem!1),
% 1.24/1.46 inference(symmetry,[status(thm)],[1063])).
% 1.24/1.46 tff(1375,plain,
% 1.24/1.46 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1374, 1069])).
% 1.24/1.46 tff(1376,plain,
% 1.24/1.46 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1375])).
% 1.24/1.46 tff(1377,plain,
% 1.24/1.46 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1063, 1064])).
% 1.24/1.46 tff(1378,plain,
% 1.24/1.46 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1377])).
% 1.24/1.46 tff(1379,plain,
% 1.24/1.46 ((~b(s(z), s(s(z)))) <=> (~b(elem!1, s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1378])).
% 1.24/1.46 tff(1380,plain,
% 1.24/1.46 (~b(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1239, 337, 1267, 1215, 1365])).
% 1.24/1.46 tff(1381,plain,
% 1.24/1.46 (~b(elem!1, s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.24/1.46 tff(1382,plain,
% 1.24/1.46 (r(elem!1, s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1015, 1381, 981])).
% 1.24/1.46 tff(1383,plain,
% 1.24/1.46 (r(s(z), s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1382, 1376])).
% 1.24/1.46 tff(1384,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1385,plain,
% 1.24/1.46 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(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(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1386,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1385])).
% 1.24/1.46 tff(1387,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1386, 1384])).
% 1.24/1.46 tff(1388,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1389,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.24/1.46 tff(1390,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1389, 189, 1383, 1373])).
% 1.24/1.46 tff(1391,plain,
% 1.24/1.46 (b(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[46, 43, 33, 1390])).
% 1.24/1.46 tff(1392,plain,
% 1.24/1.46 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1066, 1064])).
% 1.24/1.46 tff(1393,plain,
% 1.24/1.46 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1066])).
% 1.24/1.46 tff(1394,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1393, 1069])).
% 1.24/1.46 tff(1395,plain,
% 1.24/1.46 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1394])).
% 1.24/1.46 tff(1396,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.46 tff(1397,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.24/1.46 tff(1398,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1371, 337, 1396, 1274, 1342, 1341])).
% 1.24/1.46 tff(1399,plain,
% 1.24/1.46 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1360, 43, 458, 1398])).
% 1.24/1.46 tff(1400,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1401,plain,
% 1.24/1.46 (((~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(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1402,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1401])).
% 1.24/1.46 tff(1403,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.24/1.46 tff(1404,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1405,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.24/1.46 tff(1406,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1405, 189, 1339, 1397, 1399])).
% 1.24/1.46 tff(1407,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (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(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1408,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1407, 1396, 458, 1397, 1274, 1181, 1115])).
% 1.24/1.46 tff(1409,plain,
% 1.24/1.46 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[548, 1408])).
% 1.24/1.46 tff(1410,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1411,plain,
% 1.24/1.46 (((~b(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(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(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(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1412,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(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(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1411])).
% 1.24/1.46 tff(1413,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(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(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.24/1.46 tff(1414,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1415,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.24/1.46 tff(1416,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1415, 337, 1275, 1409, 1231, 1396])).
% 1.24/1.46 tff(1417,plain,
% 1.24/1.46 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1360, 43, 458, 1416])).
% 1.24/1.46 tff(1418,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1281, 337, 1275, 1409, 1231])).
% 1.24/1.46 tff(1419,plain,
% 1.24/1.46 (r(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[46, 43, 33, 1418])).
% 1.24/1.46 tff(1420,plain,
% 1.24/1.46 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1268, 1102])).
% 1.24/1.46 tff(1421,plain,
% 1.24/1.46 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1420])).
% 1.24/1.46 tff(1422,plain,
% 1.24/1.46 (~b(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1239, 337, 1275, 1231, 1396])).
% 1.24/1.46 tff(1423,plain,
% 1.24/1.46 (~b(elem!1, s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1422, 1218])).
% 1.24/1.46 tff(1424,plain,
% 1.24/1.46 (r(elem!1, s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1015, 1423, 1008])).
% 1.24/1.46 tff(1425,plain,
% 1.24/1.46 (r(s(z), s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1424, 1421])).
% 1.24/1.46 tff(1426,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1389, 189, 1425, 1419, 1417])).
% 1.24/1.46 tff(1427,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (elem!1 = s(elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1428,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1427, 1365, 1267, 1215, 1265, 1264, 1068, 1063, 981, 1161])).
% 1.24/1.46 tff(1429,plain,
% 1.24/1.46 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1428, 1395])).
% 1.24/1.46 tff(1430,plain,
% 1.24/1.46 (b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[363, 1429, 172])).
% 1.24/1.46 tff(1431,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1430, 1392])).
% 1.24/1.46 tff(1432,plain,
% 1.24/1.46 (b(z, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1050, 1430, 273, 82, 274, 50, 172, 275])).
% 1.24/1.46 tff(1433,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1434,plain,
% 1.24/1.47 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(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(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1435,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(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(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1434])).
% 1.24/1.47 tff(1436,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(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(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1435, 1433])).
% 1.24/1.47 tff(1437,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1438,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.24/1.47 tff(1439,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1438, 337, 1432, 1267, 1431, 1338, 1335, 1391])).
% 1.24/1.47 tff(1440,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1441,plain,
% 1.24/1.47 (s(s(s(elem!1))) = elem!1),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1440, 82, 273, 274, 50, 172, 275])).
% 1.24/1.47 tff(1442,plain,
% 1.24/1.47 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1441])).
% 1.24/1.47 tff(1443,plain,
% 1.24/1.47 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1442])).
% 1.24/1.47 tff(1444,plain,
% 1.24/1.47 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1443])).
% 1.24/1.47 tff(1445,plain,
% 1.24/1.47 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1444])).
% 1.24/1.47 tff(1446,plain,
% 1.24/1.47 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1441])).
% 1.24/1.47 tff(1447,plain,
% 1.24/1.47 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1446, 119])).
% 1.24/1.47 tff(1448,plain,
% 1.24/1.47 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1447])).
% 1.24/1.47 tff(1449,plain,
% 1.24/1.47 (~(elem!1 = s(z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[211, 1448])).
% 1.24/1.47 tff(1450,plain,
% 1.24/1.47 (b(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[322, 1449, 318])).
% 1.24/1.47 tff(1451,plain,
% 1.24/1.47 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1441])).
% 1.24/1.47 tff(1452,plain,
% 1.24/1.47 (b(s(z), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[311, 1451])).
% 1.24/1.47 tff(1453,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1443])).
% 1.24/1.47 tff(1454,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1453])).
% 1.24/1.47 tff(1455,plain,
% 1.24/1.47 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1454])).
% 1.24/1.47 tff(1456,plain,
% 1.24/1.47 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[775])).
% 1.24/1.47 tff(1457,plain,
% 1.24/1.47 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.47 inference(transitivity,[status(thm)],[687, 1456])).
% 1.24/1.47 tff(1458,plain,
% 1.24/1.47 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1457])).
% 1.24/1.47 tff(1459,plain,
% 1.24/1.47 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[162, 1458, 91, 776])).
% 1.24/1.47 tff(1460,plain,
% 1.24/1.47 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1459])).
% 1.24/1.47 tff(1461,plain,
% 1.24/1.47 (s(s(z)) = s(s(elem!1))),
% 1.24/1.47 inference(transitivity,[status(thm)],[21, 1460, 87])).
% 1.24/1.47 tff(1462,plain,
% 1.24/1.47 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1461])).
% 1.24/1.47 tff(1463,plain,
% 1.24/1.47 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1462])).
% 1.24/1.47 tff(1464,plain,
% 1.24/1.47 (s(elem!1) = s(z)),
% 1.24/1.47 inference(transitivity,[status(thm)],[111, 1463, 104])).
% 1.24/1.47 tff(1465,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[50, 1464])).
% 1.24/1.47 tff(1466,plain,((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1467,plain,
% 1.24/1.47 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1466, 1441, 50])).
% 1.24/1.47 tff(1468,plain,
% 1.24/1.47 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1467, 1455])).
% 1.24/1.47 tff(1469,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.24/1.47 tff(1470,plain,
% 1.24/1.47 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1469])).
% 1.24/1.47 tff(1471,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[829, 1470])).
% 1.24/1.47 tff(1472,plain,((~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1473,plain,
% 1.24/1.47 (~(s(s(s(z))) = elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1472, 1468])).
% 1.24/1.47 tff(1474,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.47 tff(1475,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1316, 189, 275, 1474])).
% 1.24/1.47 tff(1476,plain,
% 1.24/1.47 (b(s(s(s(z))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[46, 43, 33, 1475])).
% 1.24/1.47 tff(1477,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1478,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1479,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.24/1.47 tff(1480,plain,
% 1.24/1.47 (~r(s(s(s(z))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1479, 189, 274, 1474])).
% 1.24/1.47 tff(1481,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.24/1.47 tff(1482,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1483,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1484,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.24/1.47 tff(1485,plain,
% 1.24/1.47 (b(s(s(s(z))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 1480])).
% 1.24/1.47 tff(1486,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1487,plain,
% 1.24/1.47 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1488,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1487])).
% 1.24/1.47 tff(1489,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1488, 1486])).
% 1.24/1.47 tff(1490,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1491,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 1.24/1.47 tff(1492,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1491, 337, 327, 791, 1485, 1476])).
% 1.24/1.47 tff(1493,plain,((~r(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1494,plain,
% 1.24/1.47 (~r(s(s(s(z))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1493, 1473, 274, 1452, 275, 1450])).
% 1.24/1.47 tff(1495,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.47 tff(1496,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.47 tff(1497,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1312, 43, 178, 1496, 1495])).
% 1.24/1.47 tff(1498,plain,(b(s(s(s(z))), z) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1499,plain,
% 1.24/1.47 (b(s(s(s(z))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1498, 1494])).
% 1.24/1.47 tff(1500,plain,
% 1.24/1.47 (~b(z, elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[928, 1441, 82])).
% 1.24/1.47 tff(1501,plain,
% 1.24/1.47 (r(z, elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[921, 1500, 61])).
% 1.24/1.47 tff(1502,plain,
% 1.24/1.47 (~r(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[374, 1501, 273])).
% 1.24/1.47 tff(1503,plain,
% 1.24/1.47 (b(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[378, 43, 114, 1502])).
% 1.24/1.47 tff(1504,plain,
% 1.24/1.47 (~r(z, s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[385, 189, 1501, 273])).
% 1.24/1.47 tff(1505,plain,
% 1.24/1.47 (b(z, s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[395, 1504])).
% 1.24/1.47 tff(1506,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1507,plain,
% 1.24/1.47 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1508,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1507])).
% 1.24/1.47 tff(1509,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.24/1.47 tff(1510,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1511,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.24/1.47 tff(1512,plain,
% 1.24/1.47 (~b(s(elem!1), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1511, 337, 1505, 1503, 1499])).
% 1.24/1.47 tff(1513,plain,
% 1.24/1.47 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1512, 1445])).
% 1.24/1.47 tff(1514,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1443])).
% 1.24/1.47 tff(1515,plain,
% 1.24/1.47 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1514])).
% 1.24/1.47 tff(1516,plain,
% 1.24/1.47 (~b(z, elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[928, 775, 82])).
% 1.24/1.47 tff(1517,plain,
% 1.24/1.47 (r(z, elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[921, 1516, 61])).
% 1.24/1.47 tff(1518,plain,
% 1.24/1.47 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[775])).
% 1.24/1.47 tff(1519,plain,
% 1.24/1.47 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1518, 119])).
% 1.24/1.47 tff(1520,plain,
% 1.24/1.47 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1519])).
% 1.24/1.47 tff(1521,plain,
% 1.24/1.47 (~(elem!1 = s(z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[211, 1520])).
% 1.24/1.47 tff(1522,plain,
% 1.24/1.47 (~r(s(elem!1), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[893, 1521, 273, 775, 50, 173, 791, 1517])).
% 1.24/1.47 tff(1523,plain,
% 1.24/1.47 (b(s(elem!1), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[898, 1522, 50])).
% 1.24/1.47 tff(1524,plain,
% 1.24/1.47 (b(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[322, 1521, 1075])).
% 1.24/1.47 tff(1525,plain,
% 1.24/1.47 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1466, 775, 50])).
% 1.24/1.47 tff(1526,plain,
% 1.24/1.47 (~r(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[374, 1517, 273])).
% 1.24/1.47 tff(1527,plain,
% 1.24/1.47 (b(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[378, 43, 114, 1526])).
% 1.24/1.47 tff(1528,plain,
% 1.24/1.47 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1456])).
% 1.24/1.47 tff(1529,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1528])).
% 1.24/1.47 tff(1530,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1529])).
% 1.24/1.47 tff(1531,assumption,(~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.47 tff(1532,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1528])).
% 1.24/1.47 tff(1533,plain,
% 1.24/1.47 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1532])).
% 1.24/1.47 tff(1534,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[881, 189, 273, 1169])).
% 1.24/1.47 tff(1535,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.24/1.47 tff(1536,plain,
% 1.24/1.47 (((~![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))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1537,plain,
% 1.24/1.47 ((~![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))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1538,plain,
% 1.24/1.47 ((~![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)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.24/1.47 tff(1539,plain,
% 1.24/1.47 ((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)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1538, 43])).
% 1.24/1.47 tff(1540,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1539, 1535, 1531])).
% 1.24/1.47 tff(1541,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1540, 1530])).
% 1.24/1.47 tff(1542,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1177, 1169, 274])).
% 1.24/1.47 tff(1543,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[820, 43, 817, 1542])).
% 1.24/1.47 tff(1544,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.24/1.47 tff(1545,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1546,plain,
% 1.24/1.47 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1547,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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(X1, 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(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1546])).
% 1.24/1.47 tff(1548,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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(X1, 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(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1547, 1545])).
% 1.24/1.47 tff(1549,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1550,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.24/1.47 tff(1551,plain,
% 1.24/1.47 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1550, 337, 600, 1544, 599, 1543])).
% 1.24/1.47 tff(1552,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1551, 1541])).
% 1.24/1.47 tff(1553,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1554,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1553, 775, 600, 1523, 1527, 1525, 273, 274])).
% 1.24/1.47 tff(1555,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1528])).
% 1.24/1.47 tff(1556,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1555])).
% 1.24/1.47 tff(1557,plain,
% 1.24/1.47 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1528])).
% 1.24/1.47 tff(1558,plain,
% 1.24/1.47 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1557])).
% 1.24/1.47 tff(1559,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(1560,plain,
% 1.24/1.47 (s(s(s(s(z)))) = z),
% 1.24/1.47 inference(symmetry,[status(thm)],[1559])).
% 1.24/1.47 tff(1561,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[817, 1560])).
% 1.24/1.47 tff(1562,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1563,plain,
% 1.24/1.47 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[801, 1521, 775])).
% 1.24/1.47 tff(1564,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[857, 803, 1563])).
% 1.24/1.47 tff(1565,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1566,plain,
% 1.24/1.47 (((~b(s(z), elem!1)) | (~b(s(s(s(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(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1567,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1566])).
% 1.24/1.47 tff(1568,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1567, 1565])).
% 1.24/1.48 tff(1569,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(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)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1570,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 1.24/1.48 tff(1571,plain,
% 1.24/1.48 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1570, 337, 327, 791, 1564])).
% 1.24/1.48 tff(1572,plain,
% 1.24/1.48 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1150, 1571])).
% 1.24/1.48 tff(1573,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1574,plain,
% 1.24/1.48 (((~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)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1575,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1574])).
% 1.24/1.48 tff(1576,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1575, 1573])).
% 1.24/1.48 tff(1577,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1578,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.24/1.48 tff(1579,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1578, 189, 173, 1141, 1115])).
% 1.24/1.48 tff(1580,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1581,plain,
% 1.24/1.48 (~r(z, s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1580, 1572, 173])).
% 1.24/1.48 tff(1582,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1583,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1584,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.24/1.48 tff(1585,plain,
% 1.24/1.48 (b(z, s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1584, 43, 1581, 1562])).
% 1.24/1.48 tff(1586,plain,
% 1.24/1.48 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[864, 337, 327, 791, 1564])).
% 1.24/1.48 tff(1587,plain,
% 1.24/1.48 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[851, 1586])).
% 1.24/1.48 tff(1588,plain,
% 1.24/1.48 (~r(s(s(s(s(z)))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[814, 189, 173, 1587])).
% 1.24/1.48 tff(1589,plain,
% 1.24/1.48 (b(s(s(s(s(z)))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[820, 43, 817, 1588])).
% 1.24/1.48 tff(1590,plain,
% 1.24/1.48 (~(s(s(s(z))) = elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1472, 810])).
% 1.24/1.48 tff(1591,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.48 tff(1592,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.48 tff(1593,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1594,plain,
% 1.24/1.48 (((~b(z, s(s(s(s(z)))))) | (~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(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)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1595,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1594])).
% 1.24/1.48 tff(1596,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1595, 1593])).
% 1.24/1.48 tff(1597,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1598,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 1.24/1.48 tff(1599,plain,
% 1.24/1.48 (~b(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1598, 337, 2, 1592, 1591])).
% 1.24/1.48 tff(1600,plain,
% 1.24/1.48 (r(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1312, 43, 178, 1599])).
% 1.24/1.48 tff(1601,plain,
% 1.24/1.48 (~r(s(s(s(z))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1479, 189, 274, 1600])).
% 1.24/1.48 tff(1602,plain,
% 1.24/1.48 (b(s(s(s(z))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 1601])).
% 1.24/1.48 tff(1603,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(1604,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1605,plain,
% 1.24/1.48 (((~b(s(z), elem!1)) | (~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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1606,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1605])).
% 1.24/1.48 tff(1607,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.24/1.48 tff(1608,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1609,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.24/1.48 tff(1610,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1609, 337, 327, 791, 2, 1603, 1602])).
% 1.24/1.48 tff(1611,plain,((~b(s(s(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)) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1612,plain,
% 1.24/1.48 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1611, 1590, 791, 1564, 1589, 274, 1585, 327])).
% 1.24/1.48 tff(1613,plain,
% 1.24/1.48 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[548, 1612])).
% 1.24/1.48 tff(1614,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1615,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1616,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 1.24/1.48 tff(1617,plain,
% 1.24/1.48 (~r(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1616, 189, 1572, 1613])).
% 1.24/1.48 tff(1618,plain,
% 1.24/1.48 (b(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[46, 43, 33, 1617])).
% 1.24/1.48 tff(1619,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1620,plain,
% 1.24/1.48 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1621,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1620])).
% 1.24/1.48 tff(1622,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.24/1.48 tff(1623,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1624,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.24/1.48 tff(1625,plain,
% 1.24/1.48 (~b(s(elem!1), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1624, 337, 327, 1544, 791, 1618])).
% 1.24/1.48 tff(1626,plain,
% 1.24/1.48 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1625, 1558])).
% 1.24/1.48 tff(1627,plain,
% 1.24/1.48 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[612, 1626, 594])).
% 1.24/1.48 tff(1628,plain,
% 1.24/1.48 (r(s(elem!1), s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1627, 1556])).
% 1.24/1.48 tff(1629,plain,
% 1.24/1.48 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1630,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1629])).
% 1.24/1.48 tff(1631,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1630, 1486])).
% 1.24/1.48 tff(1632,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1633,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 1.24/1.48 tff(1634,plain,
% 1.24/1.48 (~b(s(s(s(z))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1633, 337, 327, 791, 1618])).
% 1.24/1.48 tff(1635,plain,
% 1.24/1.48 (r(s(s(s(z))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1484, 43, 1590, 1634])).
% 1.24/1.48 tff(1636,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1637,plain,
% 1.24/1.48 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1638,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1637])).
% 1.24/1.48 tff(1639,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1638, 1636])).
% 1.24/1.48 tff(1640,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1641,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 1.24/1.49 tff(1642,plain,
% 1.24/1.49 (~r(s(elem!1), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1641, 189, 273, 1635])).
% 1.24/1.49 tff(1643,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1642, 1628])).
% 1.24/1.49 tff(1644,plain,(r(s(s(s(s(z)))), elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1645,plain,
% 1.24/1.49 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1644, 1554, 273, 775, 1524, 1523, 791, 274, 173])).
% 1.24/1.49 tff(1646,plain,
% 1.24/1.49 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1645])).
% 1.24/1.49 tff(1647,plain,
% 1.24/1.49 (s(s(s(z))) = s(elem!1)),
% 1.24/1.49 inference(transitivity,[status(thm)],[1646, 1456])).
% 1.24/1.49 tff(1648,plain,
% 1.24/1.49 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.49 tff(1649,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1648])).
% 1.24/1.49 tff(1650,plain,
% 1.24/1.49 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.49 tff(1651,plain,
% 1.24/1.49 (s(s(z)) = s(s(s(elem!1)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[21, 1650, 91, 776])).
% 1.24/1.49 tff(1652,plain,
% 1.24/1.49 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1651])).
% 1.24/1.49 tff(1653,plain,
% 1.24/1.49 (s(z) = s(s(s(s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[105, 1652, 87, 1649])).
% 1.24/1.49 tff(1654,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[516, 1653])).
% 1.24/1.49 tff(1655,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | r(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1656,plain,
% 1.24/1.49 (~r(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1655, 1505, 273, 274, 1441, 1452, 50, 318, 82])).
% 1.24/1.49 tff(1657,plain,
% 1.24/1.49 (b(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[80, 1656])).
% 1.24/1.49 tff(1658,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.49 tff(1659,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.49 tff(1660,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1661,plain,
% 1.24/1.49 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1662,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1661])).
% 1.24/1.49 tff(1663,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.24/1.49 tff(1664,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1665,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.24/1.49 tff(1666,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1665, 337, 327, 791, 1301, 1659, 1658])).
% 1.24/1.49 tff(1667,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1668,plain,
% 1.24/1.49 (~b(s(s(s(z))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1667, 1450, 1452, 1657, 1499])).
% 1.24/1.49 tff(1669,plain,
% 1.24/1.49 (r(s(s(s(z))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[46, 43, 33, 1668])).
% 1.24/1.49 tff(1670,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1671,plain,
% 1.24/1.49 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1672,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1671])).
% 1.24/1.49 tff(1673,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1672, 1670])).
% 1.24/1.49 tff(1674,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1675,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 1.24/1.49 tff(1676,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1675, 337, 327, 1544, 791, 1301, 599])).
% 1.24/1.49 tff(1677,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1678,plain,
% 1.24/1.49 (~b(s(elem!1), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1677, 1450, 1452, 1657, 1503])).
% 1.24/1.49 tff(1679,plain,
% 1.24/1.49 (r(s(elem!1), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[898, 1678, 50])).
% 1.24/1.49 tff(1680,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1681,plain,
% 1.24/1.49 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1682,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1681])).
% 1.24/1.49 tff(1683,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1682, 1680])).
% 1.24/1.49 tff(1684,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1685,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 1.24/1.49 tff(1686,plain,
% 1.24/1.49 (~r(s(elem!1), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1685, 189, 1679, 1669])).
% 1.24/1.49 tff(1687,plain,
% 1.24/1.49 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1686, 1515])).
% 1.24/1.49 tff(1688,plain,
% 1.24/1.49 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[612, 1687, 1513])).
% 1.24/1.49 tff(1689,plain,
% 1.24/1.49 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1688])).
% 1.24/1.49 tff(1690,plain,
% 1.24/1.49 (s(s(s(z))) = s(elem!1)),
% 1.24/1.49 inference(transitivity,[status(thm)],[1689, 1442])).
% 1.24/1.49 tff(1691,plain,
% 1.24/1.49 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1690])).
% 1.24/1.49 tff(1692,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1691])).
% 1.24/1.49 tff(1693,plain,
% 1.24/1.49 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1441])).
% 1.24/1.49 tff(1694,plain,
% 1.24/1.49 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1690])).
% 1.24/1.49 tff(1695,plain,
% 1.24/1.49 (s(s(z)) = s(s(s(elem!1)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[21, 1694, 91, 1693])).
% 1.24/1.49 tff(1696,plain,
% 1.24/1.49 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1695])).
% 1.24/1.49 tff(1697,plain,
% 1.24/1.49 (s(z) = s(s(s(s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[105, 1696, 87, 1692])).
% 1.24/1.49 tff(1698,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[516, 1697])).
% 1.24/1.49 tff(1699,plain,(b(z, s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1700,plain,
% 1.24/1.49 (~r(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1699, 274, 82, 273, 50, 172])).
% 1.24/1.49 tff(1701,plain,
% 1.24/1.49 (b(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[963, 1700])).
% 1.24/1.49 tff(1702,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1703,plain,
% 1.24/1.49 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1704,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1703])).
% 1.24/1.49 tff(1705,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.24/1.49 tff(1706,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1707,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.24/1.49 tff(1708,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1707, 189, 274, 777, 173])).
% 1.24/1.49 tff(1709,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1710,plain,
% 1.24/1.49 (~r(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1709, 274, 173])).
% 1.24/1.49 tff(1711,plain,
% 1.24/1.49 (b(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[322, 1710, 247])).
% 1.24/1.49 tff(1712,plain,
% 1.24/1.49 (~(s(s(s(elem!1))) = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[928, 925, 82])).
% 1.24/1.49 tff(1713,plain,
% 1.24/1.49 (~(elem!1 = s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[281, 1712])).
% 1.24/1.49 tff(1714,plain,
% 1.24/1.49 (~r(elem!1, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[291, 274, 147])).
% 1.24/1.49 tff(1715,plain,
% 1.24/1.49 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[295, 43, 1714])).
% 1.24/1.49 tff(1716,plain,
% 1.24/1.49 (b(elem!1, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1715, 1713])).
% 1.24/1.49 tff(1717,plain,
% 1.24/1.49 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[972, 1716, 925, 327])).
% 1.24/1.49 tff(1718,plain,
% 1.24/1.49 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[350, 1717, 1712])).
% 1.24/1.49 tff(1719,plain,
% 1.24/1.49 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[358, 1718, 273])).
% 1.24/1.49 tff(1720,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[363, 1719, 172])).
% 1.24/1.49 tff(1721,plain,
% 1.24/1.49 (~b(elem!1, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1006, 1720, 273, 1714, 428, 1712, 1717])).
% 1.24/1.49 tff(1722,plain,
% 1.24/1.49 (r(elem!1, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1015, 1721, 981])).
% 1.24/1.49 tff(1723,plain,
% 1.24/1.49 (~r(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1032, 1722, 274])).
% 1.24/1.49 tff(1724,plain,
% 1.24/1.49 (b(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[395, 1723])).
% 1.24/1.49 tff(1725,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1726,plain,
% 1.24/1.49 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), 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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1727,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1726])).
% 1.24/1.49 tff(1728,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1727, 1725])).
% 1.24/1.49 tff(1729,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), 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))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1730,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 1.24/1.49 tff(1731,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1730, 337, 1720, 327, 1724, 1, 1716, 241])).
% 1.24/1.49 tff(1732,plain,((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1733,plain,
% 1.24/1.49 (~b(z, elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1732, 1711, 1701, 228, 274, 273, 172, 82])).
% 1.24/1.49 tff(1734,plain,
% 1.24/1.49 (r(z, elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[921, 1733, 61])).
% 1.24/1.49 tff(1735,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.24/1.49 tff(1736,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1737,plain,
% 1.24/1.49 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1738,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1737])).
% 1.24/1.49 tff(1739,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1738, 1736])).
% 1.24/1.49 tff(1740,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1741,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 1.24/1.49 tff(1742,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1741, 189, 370, 1735, 173])).
% 1.24/1.49 tff(1743,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1744,plain,
% 1.24/1.49 (~r(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1743, 1734, 173])).
% 1.24/1.49 tff(1745,plain,
% 1.24/1.49 (b(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[727, 1744, 272])).
% 1.24/1.49 tff(1746,plain,
% 1.24/1.49 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[765, 1734, 273, 172])).
% 1.24/1.49 tff(1747,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[385, 189, 370, 1077, 273])).
% 1.24/1.49 tff(1748,plain,((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1749,plain,
% 1.24/1.49 (~r(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1748, 1734, 273])).
% 1.24/1.49 tff(1750,plain,
% 1.24/1.49 (b(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[395, 1749])).
% 1.24/1.49 tff(1751,plain,
% 1.24/1.49 (~(s(s(s(elem!1))) = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1655, 1745, 273, 82, 173, 274, 50, 1710, 1750])).
% 1.24/1.49 tff(1752,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[350, 1751, 1746])).
% 1.24/1.49 tff(1753,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[772, 337, 1711, 1752, 1745, 228])).
% 1.24/1.49 tff(1754,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1755,plain,
% 1.24/1.49 (~r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1754, 271, 82, 173, 50, 172, 244])).
% 1.24/1.49 tff(1756,plain,
% 1.24/1.49 (((~![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))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1757,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1758,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 1.24/1.49 tff(1759,plain,
% 1.24/1.49 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1758, 43])).
% 1.24/1.49 tff(1760,plain,
% 1.24/1.49 (b(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1759, 1755, 68])).
% 1.24/1.49 tff(1761,plain,
% 1.24/1.49 (~r(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[785, 370, 173])).
% 1.24/1.49 tff(1762,plain,
% 1.24/1.49 (~r(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1743, 370, 173])).
% 1.24/1.49 tff(1763,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.24/1.49 tff(1764,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1765,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1766,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.24/1.49 tff(1767,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1766, 189, 173, 1474, 118])).
% 1.24/1.49 tff(1768,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1769,plain,
% 1.24/1.49 (~r(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1768, 173, 118])).
% 1.24/1.49 tff(1770,plain,
% 1.24/1.49 (b(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1498, 1769])).
% 1.24/1.49 tff(1771,plain,
% 1.24/1.49 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[122])).
% 1.24/1.49 tff(1772,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[857, 171, 229])).
% 1.24/1.49 tff(1773,plain,
% 1.24/1.49 (r(z, s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[215, 137])).
% 1.24/1.49 tff(1774,plain,
% 1.24/1.49 (~r(s(elem!1), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1748, 1773, 370])).
% 1.24/1.49 tff(1775,plain,
% 1.24/1.49 (s(elem!1) = elem!1),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[270, 1774, 266])).
% 1.24/1.49 tff(1776,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1777,plain,
% 1.24/1.49 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1778,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[1777])).
% 1.24/1.50 tff(1779,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)))),
% 1.24/1.50 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.24/1.50 tff(1780,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(1781,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.24/1.50 tff(1782,plain,
% 1.24/1.50 (~r(z, s(s(s(s(z)))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[1781, 189, 370, 1772])).
% 1.24/1.50 tff(1783,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.50 tff(1784,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.50 tff(1785,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[1584, 43, 1784, 1783, 1562])).
% 1.24/1.50 tff(1786,plain,(r(z, s(s(s(s(z))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.50 tff(1787,plain,
% 1.24/1.50 (b(z, s(s(s(s(z)))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[1786, 1782])).
% 1.24/1.50 tff(1788,plain,
% 1.24/1.50 (~r(s(s(s(s(z)))), z)),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[870, 189, 370, 1772])).
% 1.24/1.50 tff(1789,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.50 tff(1790,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.50 tff(1791,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[820, 43, 817, 1790, 1789])).
% 1.34/1.50 tff(1792,plain,(r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1793,plain,
% 1.34/1.50 (b(s(s(s(s(z)))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1792, 1788])).
% 1.34/1.50 tff(1794,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1598, 337, 2, 1592, 1591, 1659])).
% 1.34/1.50 tff(1795,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1796,plain,
% 1.34/1.50 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1795, 1793, 1659, 1787])).
% 1.34/1.50 tff(1797,plain,
% 1.34/1.50 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[548, 1796])).
% 1.34/1.50 tff(1798,plain,
% 1.34/1.50 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[264, 251])).
% 1.34/1.50 tff(1799,plain,
% 1.34/1.50 (s(s(s(elem!1))) = elem!1),
% 1.34/1.50 inference(transitivity,[status(thm)],[1798, 251])).
% 1.34/1.50 tff(1800,plain,
% 1.34/1.50 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1799])).
% 1.34/1.50 tff(1801,plain,
% 1.34/1.50 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1800])).
% 1.34/1.50 tff(1802,plain,
% 1.34/1.50 (elem!1 = s(s(s(s(elem!1))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[256, 1801])).
% 1.34/1.50 tff(1803,plain,
% 1.34/1.50 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1802])).
% 1.34/1.50 tff(1804,plain,
% 1.34/1.50 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.34/1.50 inference(symmetry,[status(thm)],[1803])).
% 1.34/1.50 tff(1805,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.50 tff(1806,plain,
% 1.34/1.50 (r(s(s(s(z))), elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 1.34/1.50 tff(1807,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1808,plain,
% 1.34/1.50 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~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)))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1809,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1808])).
% 1.34/1.50 tff(1810,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1809, 1807])).
% 1.34/1.50 tff(1811,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1812,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.34/1.50 tff(1813,plain,
% 1.34/1.50 (~r(s(s(s(z))), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1812, 189, 1339, 1169])).
% 1.34/1.50 tff(1814,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1813, 1806])).
% 1.34/1.50 tff(1815,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(s(elem!1) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1816,plain,
% 1.34/1.50 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1815, 1797, 1775, 1772])).
% 1.34/1.50 tff(1817,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(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(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1818,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1819,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.34/1.50 tff(1820,plain,
% 1.34/1.50 ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1819, 43])).
% 1.34/1.50 tff(1821,plain,
% 1.34/1.50 (b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1820, 116])).
% 1.34/1.50 tff(1822,plain,
% 1.34/1.50 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1821, 1816])).
% 1.34/1.50 tff(1823,plain,
% 1.34/1.50 (b(s(s(s(z))), elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1822, 1771])).
% 1.34/1.50 tff(1824,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(z))), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1825,plain,
% 1.34/1.50 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, 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(z))), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1826,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z))), elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1825])).
% 1.34/1.50 tff(1827,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(z))), elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.34/1.50 tff(1828,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1829,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.34/1.50 tff(1830,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1829, 337, 1763, 1787, 1793, 1659, 1823])).
% 1.34/1.50 tff(1831,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | b(s(elem!1), elem!1) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1832,plain,
% 1.34/1.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1831, 229, 1770, 266, 370, 215, 1763, 50])).
% 1.34/1.50 tff(1833,plain,
% 1.34/1.50 (~(s(elem!1) = elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[264, 1832])).
% 1.34/1.50 tff(1834,plain,
% 1.34/1.50 (r(s(elem!1), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[270, 1833, 266])).
% 1.34/1.50 tff(1835,plain,
% 1.34/1.50 (r(s(elem!1), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[270, 265, 266])).
% 1.34/1.50 tff(1836,plain,
% 1.34/1.50 (~r(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[374, 1835, 370])).
% 1.34/1.50 tff(1837,plain,
% 1.34/1.50 (b(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[378, 43, 114, 1836])).
% 1.34/1.50 tff(1838,plain,
% 1.34/1.50 (b(elem!1, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[322, 247, 1761])).
% 1.34/1.50 tff(1839,plain,
% 1.34/1.50 (b(s(z), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[727, 272, 1762])).
% 1.34/1.50 tff(1840,plain,
% 1.34/1.50 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[765, 1835, 370, 172])).
% 1.34/1.50 tff(1841,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[857, 802, 229])).
% 1.34/1.50 tff(1842,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[881, 189, 273, 1841])).
% 1.34/1.50 tff(1843,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1528])).
% 1.34/1.50 tff(1844,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1843])).
% 1.34/1.50 tff(1845,plain,
% 1.34/1.50 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1844])).
% 1.34/1.50 tff(1846,plain,
% 1.34/1.50 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1525, 1845])).
% 1.34/1.50 tff(1847,plain,
% 1.34/1.50 (b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[832, 43, 1846, 1842])).
% 1.34/1.50 tff(1848,plain,
% 1.34/1.50 (~r(z, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1748, 273, 370])).
% 1.34/1.50 tff(1849,plain,
% 1.34/1.50 (b(z, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[395, 1848])).
% 1.34/1.50 tff(1850,plain,
% 1.34/1.50 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[765, 273, 370, 172])).
% 1.34/1.50 tff(1851,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1852,plain,
% 1.34/1.50 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1853,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1852])).
% 1.34/1.50 tff(1854,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1853, 1851])).
% 1.34/1.50 tff(1855,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1856,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.34/1.50 tff(1857,plain,
% 1.34/1.50 (~r(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1856, 189, 173, 811])).
% 1.34/1.50 tff(1858,plain,
% 1.34/1.50 (b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1584, 43, 1857, 1562])).
% 1.34/1.50 tff(1859,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1860,plain,
% 1.34/1.50 (((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1861,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1860])).
% 1.34/1.50 tff(1862,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1861, 1859])).
% 1.34/1.50 tff(1863,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1864,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 1.34/1.50 tff(1865,plain,
% 1.34/1.50 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1864, 337, 1858, 599, 821])).
% 1.34/1.50 tff(1866,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[832, 43, 1865])).
% 1.34/1.50 tff(1867,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1866, 829])).
% 1.34/1.50 tff(1868,plain,
% 1.34/1.50 (~r(s(elem!1), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[841, 829, 173, 811, 599, 600])).
% 1.34/1.50 tff(1869,plain,
% 1.34/1.50 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.34/1.50 inference(symmetry,[status(thm)],[1188])).
% 1.34/1.50 tff(1870,plain,
% 1.34/1.50 ((~r(s(elem!1), s(z))) <=> (~r(s(elem!1), elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1869])).
% 1.34/1.50 tff(1871,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.34/1.50 tff(1872,plain,
% 1.34/1.50 (~r(s(elem!1), elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.34/1.50 tff(1873,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[273, 1872])).
% 1.34/1.50 tff(1874,plain,((~(elem!1 = s(z))) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1875,plain,
% 1.34/1.50 (~(elem!1 = s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1874, 1868, 273])).
% 1.34/1.50 tff(1876,plain,
% 1.34/1.50 (b(elem!1, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[322, 1875, 1075])).
% 1.34/1.50 tff(1877,plain,
% 1.34/1.50 (b(s(elem!1), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[898, 1868, 50])).
% 1.34/1.50 tff(1878,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.34/1.50 tff(1879,plain,
% 1.34/1.50 (~(s(z) = elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[249, 1875])).
% 1.34/1.50 tff(1880,plain,
% 1.34/1.50 (b(s(z), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[727, 1879, 1878])).
% 1.34/1.50 tff(1881,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1882,plain,
% 1.34/1.50 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1883,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), 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(X1, 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(elem!1, s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1882])).
% 1.34/1.50 tff(1884,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), 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(X1, 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(elem!1, s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1883, 1881])).
% 1.34/1.50 tff(1885,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1886,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.34/1.50 tff(1887,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1886, 337, 327, 1544, 791, 982])).
% 1.34/1.50 tff(1888,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1889,plain,
% 1.34/1.50 (~b(elem!1, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1888, 1880, 1877, 1876])).
% 1.34/1.51 tff(1890,plain,
% 1.34/1.51 (r(elem!1, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1015, 1889, 981])).
% 1.34/1.51 tff(1891,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1892,plain,
% 1.34/1.51 (((~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))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1893,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1892])).
% 1.34/1.51 tff(1894,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.34/1.51 tff(1895,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1896,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.34/1.51 tff(1897,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1896, 189, 1890, 1867])).
% 1.34/1.51 tff(1898,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[857, 1897, 853])).
% 1.34/1.51 tff(1899,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(1900,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.34/1.51 tff(1901,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1902,plain,
% 1.34/1.51 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1903,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1902])).
% 1.34/1.51 tff(1904,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.34/1.51 tff(1905,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1906,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.34/1.51 tff(1907,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1906, 337, 1763, 1603, 1592, 1591])).
% 1.34/1.51 tff(1908,plain,((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1909,plain,
% 1.34/1.51 (~b(elem!1, z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1908, 1898, 1858, 821])).
% 1.34/1.51 tff(1910,plain,
% 1.34/1.51 (r(elem!1, z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1759, 1909, 1900])).
% 1.34/1.51 tff(1911,plain,
% 1.34/1.51 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[684])).
% 1.34/1.51 tff(1912,plain,
% 1.34/1.51 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1911])).
% 1.34/1.51 tff(1913,plain,
% 1.34/1.51 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[116, 1912])).
% 1.34/1.51 tff(1914,plain,
% 1.34/1.51 (r(s(s(s(s(z)))), elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1644, 1913])).
% 1.34/1.51 tff(1915,plain,
% 1.34/1.51 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1914, 1910, 273, 173, 1877, 1880, 1876, 1897])).
% 1.34/1.51 tff(1916,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[350, 1915, 1899])).
% 1.34/1.51 tff(1917,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1918,plain,
% 1.34/1.51 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1919,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1918])).
% 1.34/1.51 tff(1920,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1919, 1917])).
% 1.34/1.51 tff(1921,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1922,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.34/1.51 tff(1923,plain,
% 1.34/1.51 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1922, 337, 1876, 1916, 1880, 1898])).
% 1.34/1.51 tff(1924,plain,
% 1.34/1.51 (b(z, s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1699, 1910, 273, 50, 275, 172])).
% 1.34/1.51 tff(1925,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(1926,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[760, 337, 365, 600, 1925, 599])).
% 1.34/1.51 tff(1927,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1928,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1927, 1924, 599, 600])).
% 1.34/1.51 tff(1929,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[363, 1928, 172])).
% 1.34/1.51 tff(1930,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1931,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1932,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.34/1.51 tff(1933,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1932, 189, 1929, 1867])).
% 1.34/1.51 tff(1934,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.34/1.51 tff(1935,plain,
% 1.34/1.51 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1934])).
% 1.34/1.51 tff(1936,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.51 inference(transitivity,[status(thm)],[162, 1935, 87])).
% 1.34/1.51 tff(1937,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1936])).
% 1.34/1.51 tff(1938,plain,
% 1.34/1.51 (s(s(z)) = s(elem!1)),
% 1.34/1.51 inference(transitivity,[status(thm)],[21, 1937, 110])).
% 1.34/1.51 tff(1939,plain,
% 1.34/1.51 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1938])).
% 1.34/1.51 tff(1940,plain,
% 1.34/1.51 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1939])).
% 1.34/1.51 tff(1941,plain,
% 1.34/1.51 (elem!1 = s(z)),
% 1.34/1.51 inference(transitivity,[status(thm)],[92, 1940, 104])).
% 1.34/1.51 tff(1942,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[247, 1941])).
% 1.34/1.51 tff(1943,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1944,plain,
% 1.34/1.51 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1943, 1875])).
% 1.34/1.51 tff(1945,plain,
% 1.34/1.51 (((~![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)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1946,plain,
% 1.34/1.51 ((~![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)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1947,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.34/1.51 tff(1948,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1947, 43, 1944, 1933, 1923])).
% 1.34/1.51 tff(1949,plain,((s(s(s(s(z)))) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (elem!1 = z) | (s(s(s(s(z)))) = elem!1) | r(s(z), elem!1) | r(elem!1, s(z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1950,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1949, 1846, 172, 173, 273, 275, 1850, 50, 1762, 68, 1849, 790, 1761, 802])).
% 1.34/1.51 tff(1951,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[851, 1950])).
% 1.34/1.51 tff(1952,plain,
% 1.34/1.51 (~r(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[893, 775, 247, 173, 50, 273, 1839, 370])).
% 1.34/1.51 tff(1953,plain,
% 1.34/1.51 (b(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[898, 1952, 50])).
% 1.34/1.51 tff(1954,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1955,plain,
% 1.34/1.51 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), 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(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1956,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1955])).
% 1.34/1.51 tff(1957,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.34/1.51 tff(1958,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), 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))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1959,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.34/1.51 tff(1960,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1959, 337, 1763, 1953, 1839, 1951, 790, 1847])).
% 1.34/1.51 tff(1961,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1962,plain,
% 1.34/1.51 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1961, 1835, 1763, 173, 172, 275, 50, 229, 247, 370])).
% 1.34/1.51 tff(1963,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[350, 1962, 1840, 984])).
% 1.34/1.51 tff(1964,plain,((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(z)) | (~r(z, elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1965,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1964, 275, 1763, 173, 172, 50, 229, 247, 370, 266])).
% 1.34/1.51 tff(1966,plain,
% 1.34/1.51 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[306, 275, 215])).
% 1.34/1.51 tff(1967,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(1968,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(1969,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[310, 43, 211, 1968, 1967])).
% 1.34/1.51 tff(1970,plain,(b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1971,plain,
% 1.34/1.51 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1970, 1966])).
% 1.34/1.51 tff(1972,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1973,plain,
% 1.34/1.51 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1974,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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(X1, 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), elem!1)) | (~b(elem!1, s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1973])).
% 1.34/1.51 tff(1975,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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(X1, 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), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1974, 1972])).
% 1.34/1.51 tff(1976,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), 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))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1977,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 1.34/1.51 tff(1978,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1977, 337, 327, 326, 791, 324])).
% 1.34/1.51 tff(1979,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1980,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1979, 1971, 1965, 1839, 1838])).
% 1.34/1.51 tff(1981,plain,((~r(s(z), z)) | (~b(elem!1, z)) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(z)) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1982,plain,
% 1.34/1.51 (~r(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1981, 247, 173, 172, 50, 229, 1763, 370, 266, 215])).
% 1.34/1.51 tff(1983,plain,
% 1.34/1.51 (b(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[963, 1982])).
% 1.34/1.51 tff(1984,plain,
% 1.34/1.51 (~r(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1748, 1835, 370])).
% 1.34/1.51 tff(1985,plain,
% 1.34/1.51 (b(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[395, 1984])).
% 1.34/1.51 tff(1986,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1987,plain,
% 1.34/1.51 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1988,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1987])).
% 1.34/1.52 tff(1989,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1988, 1986])).
% 1.34/1.52 tff(1990,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1991,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.34/1.52 tff(1992,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1991, 337, 1763, 1985, 1839, 1983, 1837])).
% 1.34/1.52 tff(1993,plain,((elem!1 = s(z)) | (~b(elem!1, z)) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1994,plain,
% 1.34/1.52 (elem!1 = s(z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1993, 1832, 173, 1763, 50, 229, 370, 266, 215])).
% 1.34/1.52 tff(1995,plain,
% 1.34/1.52 (s(z) = elem!1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1994, 120])).
% 1.34/1.52 tff(1996,plain,
% 1.34/1.52 (s(elem!1) = s(s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1994])).
% 1.34/1.52 tff(1997,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1996])).
% 1.34/1.52 tff(1998,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1997, 1994])).
% 1.34/1.52 tff(1999,plain,
% 1.34/1.52 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[1998])).
% 1.34/1.52 tff(2000,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[118, 1999])).
% 1.34/1.52 tff(2001,plain,
% 1.34/1.52 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[527])).
% 1.34/1.52 tff(2002,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.52 tff(2003,plain,
% 1.34/1.52 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2002])).
% 1.34/1.52 tff(2004,plain,
% 1.34/1.52 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2003])).
% 1.34/1.52 tff(2005,plain,
% 1.34/1.52 (s(s(s(z))) = s(s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2002])).
% 1.34/1.52 tff(2006,plain,
% 1.34/1.52 (s(s(s(z))) = s(z)),
% 1.34/1.52 inference(transitivity,[status(thm)],[2005, 21, 2004, 104])).
% 1.34/1.52 tff(2007,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[33, 2006])).
% 1.34/1.52 tff(2008,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2009,plain,
% 1.34/1.52 (~(s(s(s(z))) = s(s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2008, 2001])).
% 1.34/1.52 tff(2010,plain,
% 1.34/1.52 ((~r(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[485, 2009])).
% 1.34/1.52 tff(2011,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2010, 2000, 1995, 1834, 370])).
% 1.34/1.52 tff(2012,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(elem!1, z)) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2013,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2012, 370, 118, 173, 1763, 50, 266, 215])).
% 1.34/1.52 tff(2014,plain,
% 1.34/1.52 (b(s(z), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[727, 272, 1878])).
% 1.34/1.52 tff(2015,plain,
% 1.34/1.52 (b(elem!1, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[322, 247, 1075])).
% 1.34/1.52 tff(2016,plain,
% 1.34/1.52 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1570, 337, 2015, 2014, 1603])).
% 1.34/1.52 tff(2017,plain,
% 1.34/1.52 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1150, 2016])).
% 1.34/1.52 tff(2018,plain,
% 1.34/1.52 (~r(z, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1580, 2017, 173])).
% 1.34/1.52 tff(2019,plain,
% 1.34/1.52 (b(z, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1786, 2018])).
% 1.34/1.52 tff(2020,plain,
% 1.34/1.52 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[864, 337, 2015, 2014, 1603])).
% 1.34/1.52 tff(2021,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[851, 2020])).
% 1.34/1.52 tff(2022,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[814, 189, 173, 811, 1168])).
% 1.34/1.52 tff(2023,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2024,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2023, 2021, 173])).
% 1.34/1.52 tff(2025,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1792, 2024])).
% 1.34/1.52 tff(2026,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1616, 189, 1141, 1339, 118])).
% 1.34/1.52 tff(2027,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2028,plain,
% 1.34/1.52 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2027, 2017, 118])).
% 1.34/1.52 tff(2029,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[548, 2028])).
% 1.34/1.52 tff(2030,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1795, 2029, 2025, 1770, 2019])).
% 1.34/1.52 tff(2031,plain,((elem!1 = s(z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2032,plain,
% 1.34/1.52 (elem!1 = s(z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2031, 2013, 118, 173, 1762, 1761])).
% 1.34/1.52 tff(2033,plain,
% 1.34/1.52 (s(z) = elem!1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2032, 120])).
% 1.34/1.52 tff(2034,plain,
% 1.34/1.52 (s(elem!1) = s(s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2032])).
% 1.34/1.52 tff(2035,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2034])).
% 1.34/1.52 tff(2036,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2035, 2032])).
% 1.34/1.52 tff(2037,plain,
% 1.34/1.52 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[2036])).
% 1.34/1.52 tff(2038,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[118, 2037])).
% 1.34/1.52 tff(2039,plain,
% 1.34/1.52 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2032])).
% 1.34/1.52 tff(2040,plain,
% 1.34/1.52 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[2039])).
% 1.34/1.52 tff(2041,plain,
% 1.34/1.52 ((~(s(elem!1) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2040])).
% 1.34/1.52 tff(2042,plain,
% 1.34/1.52 (~(s(elem!1) = elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[50, 2041])).
% 1.34/1.52 tff(2043,plain,
% 1.34/1.52 (r(s(elem!1), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[270, 2042, 266])).
% 1.34/1.52 tff(2044,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2010, 2043, 2038, 2033, 370])).
% 1.34/1.52 tff(2045,plain,((~r(z, elem!1)) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2046,plain,
% 1.34/1.52 (~r(z, elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2045, 1760, 118, 50, 173, 266, 147])).
% 1.34/1.52 tff(2047,plain,
% 1.34/1.52 (b(z, elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[921, 2046, 61])).
% 1.34/1.52 tff(2048,plain,
% 1.34/1.52 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[928, 2047, 82])).
% 1.34/1.52 tff(2049,plain,
% 1.34/1.52 (elem!1 = s(s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[157])).
% 1.34/1.52 tff(2050,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2049])).
% 1.34/1.52 tff(2051,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[2050])).
% 1.34/1.52 tff(2052,plain,
% 1.34/1.52 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2049])).
% 1.34/1.52 tff(2053,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[2052])).
% 1.34/1.52 tff(2054,plain,
% 1.34/1.52 (r(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1339, 2053])).
% 1.34/1.52 tff(2055,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2056,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2057,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.34/1.52 tff(2058,plain,
% 1.34/1.52 (~r(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2057, 189, 1735, 118])).
% 1.34/1.52 tff(2059,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2058, 2054])).
% 1.34/1.52 tff(2060,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2061,plain,
% 1.34/1.52 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2060, 118, 1735, 157])).
% 1.34/1.52 tff(2062,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[548, 2061])).
% 1.34/1.52 tff(2063,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2062, 2051])).
% 1.34/1.52 tff(2064,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2065,plain,
% 1.34/1.52 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2066,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2065])).
% 1.34/1.52 tff(2067,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2066, 2064])).
% 1.34/1.52 tff(2068,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2069,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 1.34/1.52 tff(2070,plain,
% 1.34/1.52 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2069, 337, 925, 1763])).
% 1.34/1.52 tff(2071,plain,
% 1.34/1.52 (~b(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2070, 2063])).
% 1.34/1.52 tff(2072,plain,
% 1.34/1.52 (r(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1498, 2071])).
% 1.34/1.52 tff(2073,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1766, 189, 173, 2072, 118])).
% 1.34/1.52 tff(2074,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2075,plain,
% 1.34/1.52 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2074, 1735, 118, 1763, 925, 173])).
% 1.34/1.52 tff(2076,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[857, 2075, 229])).
% 1.34/1.52 tff(2077,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2078,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2079,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.34/1.52 tff(2080,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2079, 189, 1735, 2076])).
% 1.34/1.52 tff(2081,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[851, 2080])).
% 1.34/1.52 tff(2082,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2083,plain,
% 1.34/1.52 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2084,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2083])).
% 1.34/1.52 tff(2085,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2084, 2082])).
% 1.34/1.52 tff(2086,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2087,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.34/1.52 tff(2088,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2087, 189, 1735, 1141, 1169])).
% 1.34/1.52 tff(2089,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2090,plain,
% 1.34/1.52 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2089, 2076, 1735])).
% 1.34/1.52 tff(2091,plain,
% 1.34/1.52 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1150, 2090])).
% 1.34/1.52 tff(2092,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2093,plain,
% 1.34/1.52 (((~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))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2094,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2093])).
% 1.34/1.52 tff(2095,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2094, 2092])).
% 1.34/1.52 tff(2096,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2097,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 1.34/1.52 tff(2098,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2097, 189, 273, 788, 1735])).
% 1.34/1.52 tff(2099,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2100,plain,
% 1.34/1.52 (~r(s(elem!1), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2099, 1735, 273])).
% 1.34/1.52 tff(2101,plain,
% 1.34/1.52 (b(s(elem!1), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[898, 2100, 50])).
% 1.34/1.52 tff(2102,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2103,plain,
% 1.34/1.52 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2104,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2103])).
% 1.34/1.52 tff(2105,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.34/1.52 tff(2106,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2107,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.34/1.52 tff(2108,plain,
% 1.34/1.52 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2107, 337, 2101, 2091, 2081])).
% 1.34/1.52 tff(2109,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[881, 189, 273, 2076])).
% 1.34/1.52 tff(2110,plain,
% 1.34/1.52 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[832, 43, 2109])).
% 1.34/1.52 tff(2111,plain,
% 1.34/1.52 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2110, 2108])).
% 1.34/1.52 tff(2112,plain,
% 1.34/1.52 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2111])).
% 1.34/1.52 tff(2113,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2112])).
% 1.34/1.52 tff(2114,plain,
% 1.34/1.52 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(2115,plain,
% 1.34/1.52 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[2114])).
% 1.34/1.52 tff(2116,plain,
% 1.34/1.52 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2111])).
% 1.34/1.52 tff(2117,plain,
% 1.34/1.52 (s(s(s(z))) = elem!1),
% 1.34/1.52 inference(transitivity,[status(thm)],[162, 2116, 91])).
% 1.34/1.52 tff(2118,plain,
% 1.34/1.52 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2117])).
% 1.34/1.52 tff(2119,plain,
% 1.34/1.52 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.52 inference(transitivity,[status(thm)],[2118, 2115])).
% 1.34/1.52 tff(2120,plain,
% 1.34/1.52 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2119])).
% 1.34/1.52 tff(2121,plain,
% 1.34/1.52 (~(s(s(z)) = elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2009, 2120])).
% 1.34/1.52 tff(2122,plain,
% 1.34/1.52 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2111])).
% 1.34/1.52 tff(2123,plain,
% 1.34/1.52 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2122])).
% 1.34/1.52 tff(2124,plain,
% 1.34/1.52 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2123])).
% 1.34/1.52 tff(2125,plain,
% 1.34/1.52 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2122])).
% 1.34/1.52 tff(2126,plain,
% 1.34/1.52 ((~b(s(s(z)), s(elem!1))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2125])).
% 1.34/1.52 tff(2127,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2128,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2129,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.34/1.52 tff(2130,plain,
% 1.34/1.52 (~r(s(z), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2129, 189, 273, 1735])).
% 1.34/1.52 tff(2131,plain,
% 1.34/1.52 (((~![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)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2132,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2133,plain,
% 1.34/1.52 ((~![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))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.34/1.52 tff(2134,plain,
% 1.34/1.52 (b(s(z), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2133, 43, 2130, 55])).
% 1.34/1.52 tff(2135,plain,
% 1.34/1.52 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2117])).
% 1.34/1.52 tff(2136,plain,
% 1.34/1.52 (r(elem!1, s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[118, 2135])).
% 1.34/1.52 tff(2137,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2138,plain,
% 1.34/1.52 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~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(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2139,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2138])).
% 1.34/1.52 tff(2140,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2139, 2137])).
% 1.34/1.52 tff(2141,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~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))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2142,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 1.34/1.53 tff(2143,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2142, 337, 365, 1544, 324, 241])).
% 1.34/1.53 tff(2144,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2145,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2144, 1183, 324, 1544])).
% 1.34/1.53 tff(2146,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2147,plain,
% 1.34/1.53 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2148,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2147])).
% 1.34/1.53 tff(2149,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2148, 2146])).
% 1.34/1.53 tff(2150,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2151,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 1.34/1.53 tff(2152,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2151, 189, 777, 352, 214])).
% 1.34/1.53 tff(2153,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2154,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2153, 352, 777])).
% 1.34/1.53 tff(2155,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[227, 43, 2154, 2145, 213])).
% 1.34/1.53 tff(2156,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2157,plain,
% 1.34/1.53 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2156, 352, 273, 172, 1544, 777])).
% 1.34/1.53 tff(2158,plain,
% 1.34/1.53 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1970, 2157])).
% 1.34/1.53 tff(2159,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2160,plain,
% 1.34/1.53 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2161,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2160])).
% 1.34/1.53 tff(2162,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2161, 2159])).
% 1.34/1.53 tff(2163,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2164,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.34/1.53 tff(2165,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2164, 189, 352, 1735, 2158])).
% 1.34/1.53 tff(2166,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2167,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2166, 1735, 273, 172, 2101, 2136])).
% 1.34/1.53 tff(2168,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[350, 2167, 276])).
% 1.34/1.53 tff(2169,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2170,plain,
% 1.34/1.53 (((~b(z, elem!1)) | (~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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2171,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2170])).
% 1.34/1.53 tff(2172,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.34/1.53 tff(2173,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2174,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.34/1.53 tff(2175,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2174, 337, 925, 1763, 2168])).
% 1.34/1.53 tff(2176,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[406, 43, 133, 2175])).
% 1.34/1.53 tff(2177,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.34/1.53 tff(2178,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2179,plain,
% 1.34/1.53 (((~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))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2180,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2179])).
% 1.34/1.53 tff(2181,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.34/1.53 tff(2182,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2183,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.34/1.53 tff(2184,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2183, 189, 2177, 173, 214])).
% 1.34/1.53 tff(2185,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2186,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2185, 2176, 173])).
% 1.34/1.53 tff(2187,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[227, 43, 2186, 213])).
% 1.34/1.53 tff(2188,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2189,plain,
% 1.34/1.53 (((~b(s(elem!1), s(z))) | (~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(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2190,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2189])).
% 1.34/1.53 tff(2191,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2190, 2188])).
% 1.34/1.53 tff(2192,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~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))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2193,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.34/1.53 tff(2194,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2193, 337, 2101, 2187, 2134])).
% 1.34/1.53 tff(2195,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[363, 2194, 172])).
% 1.34/1.53 tff(2196,plain,
% 1.34/1.53 (~r(z, s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1082, 2195, 215])).
% 1.34/1.53 tff(2197,plain,
% 1.34/1.53 (b(z, s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[395, 2196])).
% 1.34/1.53 tff(2198,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2199,plain,
% 1.34/1.53 (((~b(s(z), s(elem!1))) | (~b(z, 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(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2200,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2199])).
% 1.34/1.53 tff(2201,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2200, 2198])).
% 1.34/1.53 tff(2202,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2203,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.34/1.53 tff(2204,plain,
% 1.34/1.53 (~b(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2203, 337, 2197, 2101, 2134])).
% 1.34/1.53 tff(2205,plain,
% 1.34/1.53 (r(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[963, 2204])).
% 1.34/1.53 tff(2206,plain,
% 1.34/1.53 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[306, 2205, 215])).
% 1.34/1.53 tff(2207,plain,
% 1.34/1.53 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1970, 2206])).
% 1.34/1.53 tff(2208,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(2209,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(2210,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2211,plain,
% 1.34/1.53 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2212,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2211])).
% 1.34/1.53 tff(2213,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2212, 2210])).
% 1.34/1.53 tff(2214,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2215,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.34/1.53 tff(2216,plain,
% 1.34/1.53 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2215, 337, 1544, 324, 2209])).
% 1.34/1.53 tff(2217,plain,
% 1.34/1.53 (~b(s(s(z)), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2216, 2208])).
% 1.34/1.53 tff(2218,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.34/1.53 tff(2219,plain,
% 1.34/1.53 (s(z) = s(s(z))),
% 1.34/1.53 inference(symmetry,[status(thm)],[2218])).
% 1.34/1.53 tff(2220,plain,
% 1.34/1.53 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2219])).
% 1.34/1.54 tff(2221,plain,
% 1.34/1.54 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2220])).
% 1.34/1.54 tff(2222,plain,
% 1.34/1.54 (s(z) = z),
% 1.34/1.54 inference(transitivity,[status(thm)],[105, 2221, 14])).
% 1.34/1.54 tff(2223,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[74, 2222])).
% 1.34/1.54 tff(2224,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2225,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2226,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2227,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.34/1.54 tff(2228,plain,
% 1.34/1.54 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2227, 43])).
% 1.34/1.54 tff(2229,plain,
% 1.34/1.54 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2228, 2224])).
% 1.34/1.54 tff(2230,plain,
% 1.34/1.54 (r(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2229, 2217])).
% 1.34/1.54 tff(2231,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2232,plain,
% 1.34/1.54 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2233,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2232])).
% 1.34/1.54 tff(2234,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2233, 2231])).
% 1.34/1.54 tff(2235,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2236,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2235, 2234])).
% 1.34/1.54 tff(2237,plain,
% 1.34/1.54 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2236, 337, 600, 1544, 2209])).
% 1.34/1.54 tff(2238,plain,
% 1.34/1.54 (~b(s(s(z)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2237, 2208])).
% 1.34/1.54 tff(2239,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.34/1.54 tff(2240,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.34/1.54 tff(2241,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1259, 43, 31, 2240, 2239])).
% 1.34/1.54 tff(2242,plain,(r(s(s(z)), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2243,plain,
% 1.34/1.54 (r(s(s(z)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2242, 2238])).
% 1.34/1.54 tff(2244,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.34/1.54 tff(2245,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.34/1.54 tff(2246,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2247,plain,
% 1.34/1.54 (((~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))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2248,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2247])).
% 1.34/1.54 tff(2249,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.34/1.54 tff(2250,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2251,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.34/1.54 tff(2252,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2251, 189, 173, 2245, 2244])).
% 1.34/1.54 tff(2253,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2254,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2253, 2243, 2230, 173])).
% 1.34/1.54 tff(2255,plain,((~b(s(s(z)), s(elem!1))) | (~r(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2256,plain,
% 1.34/1.54 (~b(s(s(z)), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2255, 2197, 173, 2101, 2134, 2207])).
% 1.34/1.54 tff(2257,plain,
% 1.34/1.54 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2256, 2126])).
% 1.34/1.54 tff(2258,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(2259,plain,
% 1.34/1.54 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2258])).
% 1.34/1.54 tff(2260,plain,
% 1.34/1.54 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2259])).
% 1.34/1.54 tff(2261,plain,
% 1.34/1.54 (s(s(s(z))) = s(z)),
% 1.34/1.54 inference(transitivity,[status(thm)],[162, 2260, 104])).
% 1.34/1.54 tff(2262,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[33, 2261])).
% 1.34/1.54 tff(2263,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2264,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2265,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2266,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 1.34/1.54 tff(2267,plain,
% 1.34/1.54 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2266, 43])).
% 1.34/1.54 tff(2268,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2267, 2263])).
% 1.34/1.54 tff(2269,plain,
% 1.34/1.54 (r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2268, 2257])).
% 1.34/1.54 tff(2270,plain,
% 1.34/1.54 (r(s(s(z)), s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2269, 2124])).
% 1.34/1.54 tff(2271,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2272,plain,
% 1.34/1.54 (((~b(s(elem!1), s(z))) | (~b(s(s(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(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2273,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(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(X1, 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(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2272])).
% 1.34/1.54 tff(2274,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(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(X1, 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(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2273, 2271])).
% 1.34/1.54 tff(2275,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(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))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2276,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 1.34/1.54 tff(2277,plain,
% 1.34/1.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2276, 337, 2101, 2187, 2134])).
% 1.34/1.54 tff(2278,plain,
% 1.34/1.54 (r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[579, 2277, 428])).
% 1.34/1.54 tff(2279,plain,
% 1.34/1.54 (~r(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1227, 2278, 215])).
% 1.34/1.54 tff(2280,plain,
% 1.34/1.54 (b(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[378, 43, 114, 2279])).
% 1.34/1.54 tff(2281,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2282,plain,
% 1.34/1.54 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2283,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2282])).
% 1.34/1.54 tff(2284,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2283, 2281])).
% 1.34/1.54 tff(2285,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2286,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 1.34/1.54 tff(2287,plain,
% 1.34/1.54 ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2286, 337, 1763, 2197, 2101])).
% 1.34/1.54 tff(2288,plain,
% 1.34/1.54 (~b(elem!1, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2287, 2280])).
% 1.34/1.54 tff(2289,plain,
% 1.34/1.54 (r(elem!1, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1015, 2288, 981])).
% 1.34/1.54 tff(2290,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2291,plain,
% 1.34/1.54 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2292,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2291])).
% 1.34/1.54 tff(2293,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2292, 2290])).
% 1.34/1.54 tff(2294,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2295,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 1.34/1.54 tff(2296,plain,
% 1.34/1.54 ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2295, 189, 2289])).
% 1.34/1.54 tff(2297,plain,
% 1.34/1.54 (~r(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2296, 2270])).
% 1.34/1.54 tff(2298,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2299,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2300,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.34/1.54 tff(2301,plain,
% 1.34/1.54 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2300, 43])).
% 1.34/1.54 tff(2302,plain,
% 1.34/1.54 (b(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2301, 2297, 2121])).
% 1.34/1.54 tff(2303,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2304,plain,
% 1.34/1.54 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2305,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2304])).
% 1.34/1.54 tff(2306,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.34/1.54 tff(2307,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2308,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.34/1.54 tff(2309,plain,
% 1.34/1.54 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2308, 337, 925, 1763, 2168, 2302])).
% 1.34/1.54 tff(2310,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2311,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2312,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 1.34/1.54 tff(2313,plain,
% 1.34/1.54 ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2312, 189, 2195])).
% 1.34/1.54 tff(2314,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2313, 2270])).
% 1.34/1.54 tff(2315,plain,
% 1.34/1.54 (((~![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)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2316,plain,
% 1.34/1.54 ((~![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)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2317,plain,
% 1.34/1.55 ((~![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))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.34/1.55 tff(2318,plain,
% 1.34/1.55 (s(s(z)) = s(s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2317, 43, 2314, 2309])).
% 1.34/1.55 tff(2319,plain,
% 1.34/1.55 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2318])).
% 1.34/1.55 tff(2320,plain,
% 1.34/1.55 (s(z) = s(s(s(s(s(z)))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[105, 2319, 87, 2113])).
% 1.34/1.55 tff(2321,plain,
% 1.34/1.55 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.34/1.55 inference(commutativity,[status(thm)],[])).
% 1.34/1.55 tff(2322,plain,
% 1.34/1.55 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2321])).
% 1.34/1.55 tff(2323,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.34/1.55 tff(2324,plain,
% 1.34/1.55 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2323])).
% 1.34/1.55 tff(2325,plain,
% 1.34/1.55 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2326,plain,
% 1.34/1.55 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2325, 12])).
% 1.34/1.55 tff(2327,plain,
% 1.34/1.55 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2326])).
% 1.34/1.55 tff(2328,plain,
% 1.34/1.55 (s(s(s(s(z)))) = z),
% 1.34/1.55 inference(transitivity,[status(thm)],[2327, 2324, 14])).
% 1.34/1.55 tff(2329,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[817, 2328])).
% 1.34/1.55 tff(2330,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2331,plain,
% 1.34/1.55 (~(s(z) = s(s(s(s(s(z))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2330, 2322])).
% 1.34/1.55 tff(2332,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2331, 2320])).
% 1.34/1.55 tff(2333,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2334,plain,
% 1.34/1.55 (~r(s(z), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2333, 2047, 172, 173, 147, 1760, 2048, 271, 118, 50, 229])).
% 1.34/1.55 tff(2335,plain,
% 1.34/1.55 (b(s(z), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[727, 2334, 250])).
% 1.34/1.55 tff(2336,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2337,plain,
% 1.34/1.55 (((~b(z, elem!1)) | (~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(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2338,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2337])).
% 1.34/1.55 tff(2339,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2338, 2336])).
% 1.34/1.55 tff(2340,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2341,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 1.34/1.55 tff(2342,plain,
% 1.34/1.55 (~b(s(z), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2341, 337, 2047, 1760, 2335])).
% 1.34/1.55 tff(2343,plain,
% 1.34/1.55 (r(s(z), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[963, 2342])).
% 1.34/1.55 tff(2344,plain,
% 1.34/1.55 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[306, 2343, 147])).
% 1.34/1.55 tff(2345,plain,
% 1.34/1.55 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1970, 2344])).
% 1.34/1.55 tff(2346,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[223, 173, 215])).
% 1.34/1.55 tff(2347,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[227, 43, 2346, 213])).
% 1.34/1.55 tff(2348,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2349,plain,
% 1.34/1.55 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2350,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2349])).
% 1.34/1.55 tff(2351,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2350, 2348])).
% 1.34/1.55 tff(2352,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2353,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 1.34/1.55 tff(2354,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2353, 189, 1077, 788, 173])).
% 1.34/1.55 tff(2355,plain,((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2356,plain,
% 1.34/1.55 (~r(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2355, 1077, 173])).
% 1.34/1.55 tff(2357,plain,
% 1.34/1.55 (b(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[898, 2356, 50])).
% 1.34/1.55 tff(2358,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2144, 2357, 1084, 2347, 324])).
% 1.34/1.55 tff(2359,plain,((~r(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2360,plain,
% 1.34/1.55 (~r(z, s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2359, 2345, 50, 172, 173, 147])).
% 1.34/1.55 tff(2361,plain,
% 1.34/1.55 (b(z, s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[395, 2360])).
% 1.34/1.55 tff(2362,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2363,plain,
% 1.34/1.55 (((~b(z, elem!1)) | (~b(s(z), 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2364,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2363])).
% 1.34/1.55 tff(2365,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2364, 2362])).
% 1.34/1.55 tff(2366,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2367,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.34/1.55 tff(2368,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2367, 337, 925, 1763, 326, 791, 241])).
% 1.34/1.55 tff(2369,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2370,plain,
% 1.34/1.55 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2369, 2047, 1760, 2335, 228])).
% 1.34/1.55 tff(2371,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[350, 2370, 2048])).
% 1.34/1.55 tff(2372,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[358, 2371, 271])).
% 1.34/1.55 tff(2373,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[363, 2372, 172])).
% 1.34/1.55 tff(2374,plain,
% 1.34/1.55 (~b(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2144, 2373, 228, 2345])).
% 1.34/1.55 tff(2375,plain,
% 1.34/1.55 (r(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[898, 2374, 50])).
% 1.34/1.55 tff(2376,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2377,plain,
% 1.34/1.55 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2378,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2377])).
% 1.34/1.55 tff(2379,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2378, 2376])).
% 1.34/1.55 tff(2380,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2381,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.34/1.55 tff(2382,plain,
% 1.34/1.55 (~r(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2381, 189, 2375, 173])).
% 1.34/1.55 tff(2383,plain,
% 1.34/1.55 (b(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[378, 43, 114, 2382])).
% 1.34/1.55 tff(2384,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, elem!1)) | (~b(s(z), 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(X1, 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), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2385,plain,
% 1.34/1.55 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~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), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2386,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~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(X1, 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), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2385])).
% 1.34/1.55 tff(2387,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~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(X1, 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), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2386, 2384])).
% 1.34/1.55 tff(2388,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2389,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 1.34/1.55 tff(2390,plain,
% 1.34/1.55 (~b(s(z), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2389, 337, 2047, 2373, 2335, 228, 2383])).
% 1.34/1.55 tff(2391,plain,
% 1.34/1.55 (~r(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2381, 189, 788, 173])).
% 1.34/1.55 tff(2392,plain,
% 1.34/1.55 (b(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[378, 43, 114, 2391])).
% 1.34/1.55 tff(2393,plain,
% 1.34/1.55 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[841, 811, 173, 788, 2392, 600])).
% 1.34/1.55 tff(2394,plain,
% 1.34/1.55 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2393])).
% 1.34/1.55 tff(2395,plain,
% 1.34/1.55 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2394])).
% 1.34/1.55 tff(2396,plain,
% 1.34/1.55 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(s(z))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2395])).
% 1.34/1.55 tff(2397,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.55 tff(2398,plain,
% 1.34/1.55 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.34/1.55 tff(2399,plain,
% 1.34/1.55 (~r(s(s(s(s(z)))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2023, 811, 173])).
% 1.34/1.55 tff(2400,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1792, 2399])).
% 1.34/1.55 tff(2401,plain,
% 1.34/1.55 (b(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1786, 1857])).
% 1.34/1.55 tff(2402,plain,
% 1.34/1.55 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1795, 2401, 1770, 2400])).
% 1.34/1.55 tff(2403,plain,
% 1.34/1.55 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[548, 2402])).
% 1.34/1.55 tff(2404,plain,
% 1.34/1.55 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2027, 2403, 118])).
% 1.34/1.55 tff(2405,plain,
% 1.34/1.55 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1150, 2404])).
% 1.34/1.55 tff(2406,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2405, 2398])).
% 1.34/1.55 tff(2407,plain,((~r(s(s(s(s(z)))), s(z))) | b(s(z), s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2408,plain,
% 1.34/1.55 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2407, 2390, 118, 173, 2375, 2361])).
% 1.34/1.55 tff(2409,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[851, 2408])).
% 1.34/1.55 tff(2410,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2411,plain,
% 1.34/1.55 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2412,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2411])).
% 1.34/1.55 tff(2413,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.34/1.55 tff(2414,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2415,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.34/1.55 tff(2416,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2415, 189, 273, 777, 788])).
% 1.34/1.55 tff(2417,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2418,plain,
% 1.34/1.55 (~r(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2417, 2375, 271])).
% 1.34/1.55 tff(2419,plain,
% 1.34/1.55 (b(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[322, 2418, 244])).
% 1.34/1.55 tff(2420,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2421,plain,
% 1.34/1.55 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), 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(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2422,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), 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(X1, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2421])).
% 1.34/1.55 tff(2423,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), 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(X1, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2422, 2420])).
% 1.34/1.55 tff(2424,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), 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))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2425,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 1.34/1.55 tff(2426,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2425, 337, 2419, 2335, 2409, 228])).
% 1.34/1.56 tff(2427,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1943, 244])).
% 1.34/1.56 tff(2428,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1947, 43, 2427, 2426])).
% 1.34/1.56 tff(2429,plain,
% 1.34/1.56 (~b(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[737, 337, 2419, 2335, 228])).
% 1.34/1.56 tff(2430,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[281, 2048])).
% 1.34/1.56 tff(2431,plain,
% 1.34/1.56 (r(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[295, 43, 2430, 2429])).
% 1.34/1.56 tff(2432,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2433,plain,
% 1.34/1.56 (((~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))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2434,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2433])).
% 1.34/1.56 tff(2435,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.34/1.56 tff(2436,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2437,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.34/1.56 tff(2438,plain,
% 1.34/1.56 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2437, 189, 2431, 2428])).
% 1.34/1.56 tff(2439,plain,
% 1.34/1.56 (s(s(s(s(z)))) = elem!1),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[857, 2438, 229])).
% 1.34/1.56 tff(2440,plain,
% 1.34/1.56 (elem!1 = s(s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2439])).
% 1.34/1.56 tff(2441,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2440])).
% 1.34/1.56 tff(2442,plain,
% 1.34/1.56 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.56 inference(symmetry,[status(thm)],[2441])).
% 1.34/1.56 tff(2443,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.34/1.56 tff(2444,plain,
% 1.34/1.56 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2443])).
% 1.34/1.56 tff(2445,plain,
% 1.34/1.56 (s(s(z)) = s(s(elem!1))),
% 1.34/1.56 inference(transitivity,[status(thm)],[21, 2444, 87])).
% 1.34/1.56 tff(2446,plain,
% 1.34/1.56 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2445])).
% 1.34/1.56 tff(2447,plain,
% 1.34/1.56 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2446])).
% 1.34/1.56 tff(2448,plain,
% 1.34/1.56 (s(elem!1) = s(z)),
% 1.34/1.56 inference(transitivity,[status(thm)],[111, 2447, 104])).
% 1.34/1.56 tff(2449,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[50, 2448])).
% 1.34/1.56 tff(2450,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2451,plain,
% 1.34/1.56 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2450, 50])).
% 1.34/1.56 tff(2452,plain,
% 1.34/1.56 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[991, 189, 271, 2371])).
% 1.34/1.56 tff(2453,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[579, 2452, 428])).
% 1.34/1.56 tff(2454,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2455,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2069, 337, 925, 1763, 1659, 2454])).
% 1.34/1.56 tff(2456,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2457,plain,
% 1.34/1.56 (~b(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2456, 2047, 1770, 1760])).
% 1.34/1.56 tff(2458,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[809, 2438, 271])).
% 1.34/1.56 tff(2459,plain,
% 1.34/1.56 (~(s(s(s(z))) = elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1472, 2458])).
% 1.34/1.56 tff(2460,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2461,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2462,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 2461, 2460])).
% 1.34/1.56 tff(2463,plain,(b(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2464,plain,
% 1.34/1.56 (r(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2463, 2459, 2457])).
% 1.34/1.56 tff(2465,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2466,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2467,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2468,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 1.34/1.56 tff(2469,plain,
% 1.34/1.56 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2468, 189, 352, 2465])).
% 1.34/1.56 tff(2470,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.56 tff(2471,plain,
% 1.34/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2472,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2473,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.34/1.56 tff(2474,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2473, 43, 2470, 2469])).
% 1.34/1.56 tff(2475,plain,
% 1.34/1.56 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[157])).
% 1.34/1.56 tff(2476,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2475])).
% 1.34/1.56 tff(2477,assumption,(~(s(s(s(z))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.56 tff(2478,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2475])).
% 1.34/1.56 tff(2479,plain,
% 1.34/1.56 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2478])).
% 1.34/1.56 tff(2480,plain,
% 1.34/1.56 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2479])).
% 1.34/1.56 tff(2481,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2482,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2483,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 1.34/1.56 tff(2484,plain,
% 1.34/1.56 (~r(s(s(s(z))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2483, 189, 273, 2465])).
% 1.34/1.56 tff(2485,plain,
% 1.34/1.56 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2484, 2480])).
% 1.34/1.56 tff(2486,plain,
% 1.34/1.56 (((~![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)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2487,plain,
% 1.34/1.56 ((~![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)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2488,plain,
% 1.34/1.56 ((~![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))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.34/1.56 tff(2489,plain,
% 1.34/1.56 ((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))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2488, 43])).
% 1.34/1.56 tff(2490,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2489, 2485, 2477])).
% 1.34/1.56 tff(2491,plain,
% 1.34/1.56 (b(s(s(s(z))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2490, 2476])).
% 1.34/1.56 tff(2492,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2493,plain,
% 1.34/1.56 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2494,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2493])).
% 1.34/1.56 tff(2495,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2494, 2492])).
% 1.34/1.56 tff(2496,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2497,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 1.34/1.56 tff(2498,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2497, 337, 365, 638, 2491, 2474])).
% 1.34/1.56 tff(2499,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(s(s(s(s(z)))) = elem!1)) | (s(s(s(z))) = s(s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2500,plain,
% 1.34/1.56 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2499, 2464, 2453, 2373, 2439, 2451, 2371, 271])).
% 1.34/1.56 tff(2501,plain,
% 1.34/1.56 (s(s(s(z))) = s(elem!1)),
% 1.34/1.56 inference(transitivity,[status(thm)],[2500, 2442])).
% 1.34/1.56 tff(2502,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2503,plain,
% 1.34/1.56 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2502])).
% 1.34/1.56 tff(2504,plain,
% 1.34/1.56 (s(s(z)) = s(s(s(s(z))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[21, 2503, 91, 2049])).
% 1.34/1.56 tff(2505,plain,
% 1.34/1.56 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2504])).
% 1.34/1.56 tff(2506,plain,
% 1.34/1.56 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2505])).
% 1.34/1.56 tff(2507,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(z)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2502])).
% 1.34/1.56 tff(2508,plain,
% 1.34/1.56 (s(elem!1) = s(z)),
% 1.34/1.56 inference(transitivity,[status(thm)],[2507, 162, 2506, 104])).
% 1.34/1.56 tff(2509,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[50, 2508])).
% 1.34/1.56 tff(2510,plain,((~(s(s(s(z))) = s(elem!1))) | (s(elem!1) = s(z)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2511,plain,
% 1.34/1.56 (~(s(s(s(z))) = s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2510, 2439, 50])).
% 1.34/1.56 tff(2512,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2511, 2501])).
% 1.34/1.56 tff(2513,plain,(b(s(elem!1), elem!1) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2514,plain,
% 1.34/1.56 (b(s(elem!1), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2513, 172, 229, 118, 173, 50, 82])).
% 1.34/1.56 tff(2515,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(2516,plain,
% 1.34/1.56 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2515])).
% 1.34/1.56 tff(2517,plain,
% 1.34/1.56 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2516])).
% 1.34/1.56 tff(2518,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1943, 247])).
% 1.34/1.56 tff(2519,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 1.34/1.56 tff(2520,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2521,plain,
% 1.34/1.56 (b(elem!1, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[322, 247, 1710])).
% 1.34/1.56 tff(2522,plain,
% 1.34/1.56 (b(elem!1, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1015, 1085, 1008])).
% 1.34/1.56 tff(2523,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2524,plain,
% 1.34/1.56 (((~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))), 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(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2525,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2524])).
% 1.34/1.56 tff(2526,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2525, 2523])).
% 1.34/1.56 tff(2527,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2528,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 1.34/1.56 tff(2529,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2528, 337, 1084, 2520, 2522, 325])).
% 1.34/1.56 tff(2530,plain,((~r(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2531,plain,
% 1.34/1.56 (~r(z, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2530, 1716, 147, 274, 172, 981, 2520])).
% 1.34/1.56 tff(2532,plain,
% 1.34/1.56 (b(z, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[395, 2531])).
% 1.34/1.56 tff(2533,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2534,plain,
% 1.34/1.56 (((~b(s(elem!1), elem!1)) | (~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(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2535,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2534])).
% 1.34/1.56 tff(2536,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2535, 2533])).
% 1.34/1.56 tff(2537,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2538,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.34/1.56 tff(2539,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2538, 337, 925, 600, 2520, 982])).
% 1.34/1.56 tff(2540,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,[]))).
% 1.34/1.56 tff(2541,plain,
% 1.34/1.56 (~b(elem!1, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2540, 2532, 2520, 925])).
% 1.34/1.56 tff(2542,plain,
% 1.34/1.56 (r(elem!1, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1015, 2541, 981])).
% 1.34/1.56 tff(2543,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.56 tff(2544,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2545,plain,
% 1.34/1.56 (((~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2546,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2545])).
% 1.34/1.56 tff(2547,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2546, 2544])).
% 1.34/1.56 tff(2548,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2549,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 1.34/1.56 tff(2550,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2549, 189, 353, 2543, 352])).
% 1.34/1.56 tff(2551,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2552,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2551, 2542, 1718])).
% 1.34/1.56 tff(2553,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[363, 2552, 172])).
% 1.34/1.56 tff(2554,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2555,plain,
% 1.34/1.56 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(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(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2556,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2555])).
% 1.34/1.56 tff(2557,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2556, 2554])).
% 1.34/1.57 tff(2558,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2559,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.34/1.57 tff(2560,plain,
% 1.34/1.57 (~b(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2559, 337, 925, 2553, 2532, 2520, 1716])).
% 1.34/1.57 tff(2561,plain,
% 1.34/1.57 (~r(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1023, 2542, 274])).
% 1.34/1.57 tff(2562,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[378, 43, 114, 2561, 2560])).
% 1.34/1.57 tff(2563,plain,((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2564,plain,
% 1.34/1.57 (~b(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2563, 2521, 172, 274, 2520, 82])).
% 1.34/1.57 tff(2565,plain,
% 1.34/1.57 (r(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[921, 2564, 61])).
% 1.34/1.57 tff(2566,plain,
% 1.34/1.57 (~r(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1743, 2565, 173])).
% 1.34/1.57 tff(2567,plain,
% 1.34/1.57 (b(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[727, 2566, 272])).
% 1.34/1.57 tff(2568,plain,
% 1.34/1.57 (~b(elem!1, s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[737, 337, 2521, 2567, 228])).
% 1.34/1.57 tff(2569,plain,
% 1.34/1.57 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1715, 2568])).
% 1.34/1.57 tff(2570,plain,
% 1.34/1.57 (s(s(s(elem!1))) = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[281, 2569])).
% 1.34/1.57 tff(2571,plain,
% 1.34/1.57 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[801, 2570, 247])).
% 1.34/1.57 tff(2572,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[857, 2571, 229])).
% 1.34/1.57 tff(2573,plain,
% 1.34/1.57 (~r(s(s(s(s(z)))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1177, 2572, 274])).
% 1.34/1.57 tff(2574,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1792, 2573])).
% 1.34/1.57 tff(2575,plain,
% 1.34/1.57 (~b(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1888, 2522, 791, 327])).
% 1.34/1.57 tff(2576,plain,
% 1.34/1.57 (r(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[898, 2575, 50])).
% 1.34/1.57 tff(2577,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2353, 189, 1077, 2576, 173])).
% 1.34/1.57 tff(2578,plain,((~r(z, s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2579,plain,
% 1.34/1.57 (~r(z, s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2578, 2567, 173, 274, 50, 981, 2521])).
% 1.34/1.57 tff(2580,plain,
% 1.34/1.57 (b(z, s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[395, 2579])).
% 1.34/1.57 tff(2581,plain,
% 1.34/1.57 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2569])).
% 1.34/1.57 tff(2582,plain,
% 1.34/1.57 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2581])).
% 1.34/1.57 tff(2583,plain,
% 1.34/1.57 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2582])).
% 1.34/1.57 tff(2584,plain,
% 1.34/1.57 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2583])).
% 1.34/1.57 tff(2585,plain,
% 1.34/1.57 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1466, 2570, 50])).
% 1.34/1.57 tff(2586,plain,
% 1.34/1.57 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.34/1.57 tff(2587,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2588,plain,
% 1.34/1.57 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2589,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2588])).
% 1.34/1.57 tff(2590,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2589, 2587])).
% 1.34/1.57 tff(2591,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2592,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 1.34/1.57 tff(2593,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2592, 337, 2015, 2520, 1544, 2014])).
% 1.34/1.57 tff(2594,plain,((elem!1 = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2595,plain,
% 1.34/1.57 (~b(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2594, 2566, 1710, 2520, 247])).
% 1.34/1.57 tff(2596,plain,
% 1.34/1.57 (r(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[898, 2595, 50])).
% 1.34/1.57 tff(2597,plain,
% 1.34/1.57 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2581])).
% 1.34/1.57 tff(2598,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), z) <=> b(s(elem!1), z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2597])).
% 1.34/1.57 tff(2599,plain,
% 1.34/1.57 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2581])).
% 1.34/1.57 tff(2600,plain,
% 1.34/1.57 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2599])).
% 1.34/1.57 tff(2601,plain,
% 1.34/1.57 (~r(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2381, 189, 2596, 173])).
% 1.34/1.57 tff(2602,plain,
% 1.34/1.57 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 1.34/1.57 tff(2603,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[663, 2602])).
% 1.34/1.57 tff(2604,plain,
% 1.34/1.57 (b(s(elem!1), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2603, 2598])).
% 1.34/1.57 tff(2605,plain,
% 1.34/1.57 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[841, 2604, 173, 2596, 2586, 2580])).
% 1.34/1.57 tff(2606,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[851, 2605])).
% 1.34/1.57 tff(2607,plain,
% 1.34/1.57 (s(s(s(elem!1))) = elem!1),
% 1.34/1.57 inference(symmetry,[status(thm)],[2569])).
% 1.34/1.57 tff(2608,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2607])).
% 1.34/1.57 tff(2609,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2608])).
% 1.34/1.57 tff(2610,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2572, 2609])).
% 1.34/1.57 tff(2611,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2612,plain,
% 1.34/1.57 (((~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))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2613,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2612])).
% 1.34/1.57 tff(2614,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2613, 2611])).
% 1.34/1.57 tff(2615,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2616,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.34/1.57 tff(2617,plain,
% 1.34/1.57 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2616, 189, 147])).
% 1.34/1.57 tff(2618,plain,
% 1.34/1.57 (~r(z, s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2617, 2610])).
% 1.34/1.57 tff(2619,plain,
% 1.34/1.57 (b(z, s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1786, 2618])).
% 1.34/1.57 tff(2620,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1795, 2619, 1770, 2574])).
% 1.34/1.57 tff(2621,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[548, 2620])).
% 1.34/1.57 tff(2622,plain,
% 1.34/1.57 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2027, 2621, 118])).
% 1.34/1.57 tff(2623,plain,
% 1.34/1.57 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1150, 2622])).
% 1.34/1.57 tff(2624,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2625,plain,
% 1.34/1.57 (((~b(s(s(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))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(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(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2626,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2625])).
% 1.34/1.57 tff(2627,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2626, 2624])).
% 1.34/1.57 tff(2628,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2629,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.34/1.57 tff(2630,plain,
% 1.34/1.57 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2629, 337, 2623, 2606, 228, 2574])).
% 1.34/1.57 tff(2631,plain,
% 1.34/1.57 (((~![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))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2632,plain,
% 1.34/1.57 ((~![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))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2633,plain,
% 1.34/1.57 ((~![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)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 1.34/1.57 tff(2634,plain,
% 1.34/1.57 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2633, 43, 2630])).
% 1.34/1.57 tff(2635,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2634, 2519])).
% 1.34/1.57 tff(2636,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2637,plain,
% 1.34/1.57 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2638,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2637])).
% 1.34/1.57 tff(2639,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.34/1.57 tff(2640,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2641,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.34/1.57 tff(2642,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2641, 189, 2621, 2635])).
% 1.34/1.57 tff(2643,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2473, 43, 2451, 2642])).
% 1.34/1.57 tff(2644,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2607])).
% 1.34/1.57 tff(2645,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2644])).
% 1.34/1.57 tff(2646,plain,
% 1.34/1.57 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2581])).
% 1.34/1.57 tff(2647,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2646, 2569])).
% 1.34/1.57 tff(2648,plain,
% 1.34/1.57 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2647])).
% 1.34/1.57 tff(2649,plain,
% 1.34/1.57 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[775])).
% 1.34/1.57 tff(2650,plain,
% 1.34/1.57 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2649])).
% 1.34/1.57 tff(2651,plain,
% 1.34/1.57 (b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2520, 2650])).
% 1.34/1.57 tff(2652,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.57 tff(2653,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2652, 2651])).
% 1.34/1.57 tff(2654,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(elem!1), s(s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2655,plain,
% 1.34/1.57 (b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2654, 2570, 2520])).
% 1.34/1.57 tff(2656,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2655, 2648])).
% 1.34/1.57 tff(2657,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2656, 2645])).
% 1.34/1.57 tff(2658,plain,
% 1.34/1.57 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2569])).
% 1.34/1.57 tff(2659,plain,
% 1.34/1.57 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2567, 2658])).
% 1.34/1.57 tff(2660,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2661,plain,
% 1.34/1.57 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2662,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2661])).
% 1.34/1.57 tff(2663,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.34/1.57 tff(2664,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2665,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.34/1.57 tff(2666,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2665, 337, 2659, 228, 2657, 2643])).
% 1.34/1.57 tff(2667,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1821, 2666])).
% 1.34/1.57 tff(2668,plain,
% 1.34/1.57 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2581])).
% 1.34/1.57 tff(2669,plain,
% 1.34/1.57 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2580, 2668])).
% 1.34/1.57 tff(2670,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2671,plain,
% 1.34/1.58 (((~b(s(s(s(s(elem!1)))), z)) | (~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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2672,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2671])).
% 1.34/1.58 tff(2673,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2672, 2670])).
% 1.34/1.58 tff(2674,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2675,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 1.34/1.58 tff(2676,plain,
% 1.34/1.58 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2675, 337, 2574, 2669, 2603])).
% 1.34/1.58 tff(2677,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1539, 2676, 2585])).
% 1.34/1.58 tff(2678,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2679,plain,
% 1.34/1.58 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(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(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2680,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2679])).
% 1.34/1.58 tff(2681,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2680, 2678])).
% 1.34/1.58 tff(2682,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2683,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 1.34/1.58 tff(2684,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2683, 189, 2621, 2677, 2667])).
% 1.34/1.58 tff(2685,plain,((elem!1 = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2686,plain,
% 1.34/1.58 (~r(elem!1, z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2685, 2514, 173, 244, 229, 118, 50, 172, 82])).
% 1.34/1.58 tff(2687,plain,
% 1.34/1.58 (b(elem!1, z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1759, 2686, 68])).
% 1.34/1.58 tff(2688,plain,
% 1.34/1.58 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2359, 1077, 50, 172, 173, 215])).
% 1.34/1.58 tff(2689,plain,
% 1.34/1.58 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1970, 2688])).
% 1.34/1.58 tff(2690,plain,
% 1.34/1.58 (~r(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[306, 2689, 215])).
% 1.34/1.58 tff(2691,plain,
% 1.34/1.58 (b(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[963, 2690])).
% 1.34/1.58 tff(2692,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(z), z)) | (~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(X1, 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(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2693,plain,
% 1.34/1.58 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2694,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), 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(X1, 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(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2693])).
% 1.34/1.58 tff(2695,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), 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(X1, 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(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.34/1.58 tff(2696,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), 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))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2697,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.34/1.58 tff(2698,plain,
% 1.34/1.58 (~b(s(z), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2697, 337, 1763, 1084, 2520, 2691, 2347])).
% 1.34/1.58 tff(2699,plain,
% 1.34/1.58 (r(s(z), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2133, 43, 2698, 55])).
% 1.34/1.58 tff(2700,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2701,plain,
% 1.34/1.58 (((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2702,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2701])).
% 1.34/1.58 tff(2703,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2702, 2700])).
% 1.34/1.58 tff(2704,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2705,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 1.34/1.58 tff(2706,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2705, 189, 1077, 173, 2699])).
% 1.34/1.58 tff(2707,plain,((~r(z, s(elem!1))) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2708,plain,
% 1.34/1.58 (~r(z, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2707, 2687, 173, 2514, 147, 172, 50])).
% 1.34/1.58 tff(2709,plain,
% 1.34/1.58 (b(z, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[395, 2708])).
% 1.34/1.58 tff(2710,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2711,plain,
% 1.34/1.58 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2712,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2711])).
% 1.34/1.58 tff(2713,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2712, 2710])).
% 1.34/1.58 tff(2714,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2715,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.34/1.58 tff(2716,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2715, 337, 925, 1763, 600, 2520])).
% 1.34/1.58 tff(2717,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2718,plain,
% 1.34/1.58 (~b(z, elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2717, 2709, 2514, 2687])).
% 1.34/1.58 tff(2719,plain,
% 1.34/1.58 (r(z, elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[921, 2718, 61])).
% 1.34/1.58 tff(2720,plain,
% 1.34/1.58 (~r(elem!1, s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[785, 2719, 173])).
% 1.34/1.58 tff(2721,plain,
% 1.34/1.58 (~r(s(z), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1743, 2719, 173])).
% 1.34/1.58 tff(2722,plain,
% 1.34/1.58 (~b(s(elem!1), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2594, 2721, 244, 2514, 2720])).
% 1.34/1.58 tff(2723,plain,
% 1.34/1.58 (r(s(elem!1), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[898, 2722, 50])).
% 1.34/1.58 tff(2724,plain,
% 1.34/1.58 (~r(s(elem!1), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2381, 189, 2723, 173])).
% 1.34/1.58 tff(2725,plain,
% 1.34/1.58 (b(s(elem!1), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[378, 43, 114, 2724])).
% 1.34/1.58 tff(2726,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2727,plain,
% 1.34/1.58 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2728,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2727])).
% 1.34/1.58 tff(2729,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2728, 2726])).
% 1.34/1.58 tff(2730,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2731,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.34/1.58 tff(2732,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2731, 337, 2687, 2709, 2514, 2725])).
% 1.34/1.58 tff(2733,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(z))), s(z))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2734,plain,
% 1.34/1.58 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2733, 229, 50, 173, 118, 82])).
% 1.34/1.58 tff(2735,plain,
% 1.34/1.58 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[804])).
% 1.34/1.58 tff(2736,plain,
% 1.34/1.58 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.58 inference(transitivity,[status(thm)],[162, 2735, 89, 87])).
% 1.34/1.58 tff(2737,plain,
% 1.34/1.58 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2736])).
% 1.34/1.58 tff(2738,plain,
% 1.34/1.58 (s(s(z)) = s(elem!1)),
% 1.34/1.58 inference(transitivity,[status(thm)],[21, 2737, 110])).
% 1.34/1.58 tff(2739,plain,
% 1.34/1.58 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2738])).
% 1.34/1.58 tff(2740,plain,
% 1.34/1.58 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2739])).
% 1.34/1.58 tff(2741,plain,
% 1.34/1.58 (elem!1 = s(z)),
% 1.34/1.58 inference(transitivity,[status(thm)],[92, 2740, 104])).
% 1.34/1.58 tff(2742,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[247, 2741])).
% 1.34/1.58 tff(2743,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (elem!1 = s(z)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2744,plain,
% 1.34/1.58 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2743, 2734, 244])).
% 1.34/1.58 tff(2745,plain,
% 1.34/1.58 (~(s(s(s(z))) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1472, 2744])).
% 1.34/1.58 tff(2746,plain,
% 1.34/1.58 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[170, 2734, 50])).
% 1.34/1.58 tff(2747,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[857, 2746, 229])).
% 1.34/1.58 tff(2748,plain,
% 1.34/1.58 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2734])).
% 1.34/1.58 tff(2749,plain,
% 1.34/1.58 (b(s(elem!1), s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[228, 2748])).
% 1.34/1.58 tff(2750,plain,
% 1.34/1.58 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2734])).
% 1.34/1.58 tff(2751,plain,
% 1.34/1.58 (r(z, s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[147, 2750])).
% 1.34/1.58 tff(2752,plain,
% 1.34/1.58 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[83])).
% 1.34/1.58 tff(2753,plain,
% 1.34/1.58 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2752])).
% 1.34/1.58 tff(2754,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.34/1.58 tff(2755,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1177, 274, 1169])).
% 1.34/1.58 tff(2756,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1792, 2755])).
% 1.34/1.58 tff(2757,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.58 tff(2758,plain,
% 1.34/1.58 (s(s(s(s(z)))) = elem!1),
% 1.34/1.58 inference(symmetry,[status(thm)],[2757])).
% 1.34/1.58 tff(2759,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[853, 2758])).
% 1.34/1.58 tff(2760,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2761,plain,
% 1.34/1.58 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2760, 171])).
% 1.34/1.58 tff(2762,plain,
% 1.34/1.58 (~r(s(elem!1), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1748, 370, 1077])).
% 1.34/1.58 tff(2763,plain,
% 1.34/1.58 (s(elem!1) = elem!1),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[270, 2762, 266])).
% 1.34/1.58 tff(2764,plain,
% 1.34/1.58 (s(s(z)) = s(elem!1)),
% 1.34/1.58 inference(transitivity,[status(thm)],[149, 256])).
% 1.34/1.58 tff(2765,plain,
% 1.34/1.58 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2764])).
% 1.34/1.58 tff(2766,plain,
% 1.34/1.58 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2765])).
% 1.34/1.58 tff(2767,plain,
% 1.34/1.58 (elem!1 = s(z)),
% 1.34/1.58 inference(transitivity,[status(thm)],[92, 2766, 104])).
% 1.34/1.58 tff(2768,plain,
% 1.34/1.58 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1799])).
% 1.34/1.58 tff(2769,plain,
% 1.34/1.58 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2768, 119])).
% 1.34/1.58 tff(2770,plain,
% 1.34/1.58 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2769])).
% 1.34/1.58 tff(2771,plain,
% 1.34/1.58 (~(elem!1 = s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[211, 2770])).
% 1.34/1.58 tff(2772,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2771, 2767])).
% 1.34/1.58 tff(2773,plain,((~(s(s(z)) = elem!1)) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2774,plain,
% 1.34/1.58 (~(s(s(z)) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2773, 2763])).
% 1.34/1.58 tff(2775,plain,
% 1.34/1.58 (b(s(z), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[727, 1762, 2754])).
% 1.34/1.58 tff(2776,plain,
% 1.34/1.58 (~r(z, s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1781, 189, 370, 1169])).
% 1.34/1.58 tff(2777,plain,
% 1.34/1.58 (b(z, s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1786, 2776])).
% 1.34/1.58 tff(2778,plain,
% 1.34/1.58 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(2779,plain,
% 1.34/1.58 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2778])).
% 1.34/1.58 tff(2780,plain,
% 1.34/1.58 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2779])).
% 1.34/1.58 tff(2781,plain,
% 1.34/1.58 (~(s(z) = s(s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[33, 2780])).
% 1.34/1.58 tff(2782,plain,
% 1.34/1.58 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1795, 2777, 1770, 1591])).
% 1.34/1.58 tff(2783,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[548, 2782])).
% 1.34/1.58 tff(2784,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1815, 2783, 2763, 1169])).
% 1.34/1.58 tff(2785,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1821, 2784])).
% 1.34/1.58 tff(2786,plain,
% 1.34/1.58 (b(s(s(s(z))), elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2785, 1771])).
% 1.34/1.58 tff(2787,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2788,plain,
% 1.34/1.59 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2789,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2788])).
% 1.34/1.59 tff(2790,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2789, 2787])).
% 1.34/1.59 tff(2791,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2792,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.34/1.59 tff(2793,plain,
% 1.34/1.59 (~b(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2792, 337, 327, 2775, 2786])).
% 1.34/1.59 tff(2794,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2795,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2796,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 1.34/1.59 tff(2797,plain,
% 1.34/1.59 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2796, 43, 2793])).
% 1.34/1.59 tff(2798,plain,
% 1.34/1.59 (r(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2797, 2781])).
% 1.34/1.59 tff(2799,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2800,plain,
% 1.34/1.59 (((~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))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2801,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2800])).
% 1.34/1.59 tff(2802,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2801, 2799])).
% 1.34/1.59 tff(2803,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2804,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 1.34/1.59 tff(2805,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2804, 337, 2777, 1591, 1770])).
% 1.34/1.59 tff(2806,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[524, 2805])).
% 1.34/1.59 tff(2807,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2808,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2809,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.34/1.59 tff(2810,plain,
% 1.34/1.59 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2809, 189, 2806, 2798])).
% 1.34/1.59 tff(2811,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[851, 2810])).
% 1.34/1.59 tff(2812,plain,
% 1.34/1.59 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2027, 2783, 118])).
% 1.34/1.59 tff(2813,plain,
% 1.34/1.59 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1150, 2812])).
% 1.34/1.59 tff(2814,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2815,plain,
% 1.34/1.59 (((~b(s(z), 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2816,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2815])).
% 1.34/1.59 tff(2817,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2816, 2814])).
% 1.34/1.59 tff(2818,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2819,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.34/1.59 tff(2820,plain,
% 1.34/1.59 (~b(s(s(z)), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2819, 337, 791, 1275, 1231, 1396])).
% 1.34/1.59 tff(2821,plain,
% 1.34/1.59 (r(s(s(z)), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2229, 2820])).
% 1.34/1.59 tff(2822,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2823,plain,
% 1.34/1.59 (((~b(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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2824,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2823])).
% 1.34/1.59 tff(2825,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2824, 2822])).
% 1.34/1.59 tff(2826,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2827,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.34/1.59 tff(2828,plain,
% 1.34/1.59 (~b(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2827, 337, 1275, 1231, 1396, 1592])).
% 1.34/1.59 tff(2829,plain,
% 1.34/1.59 (r(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2242, 2828])).
% 1.34/1.59 tff(2830,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2253, 2829, 2821, 173])).
% 1.34/1.59 tff(2831,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~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), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2832,plain,
% 1.34/1.59 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2831, 2813, 173, 2811, 2777, 2775])).
% 1.34/1.59 tff(2833,plain,
% 1.34/1.59 (r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2268, 2832])).
% 1.34/1.59 tff(2834,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), 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(X1, 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(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2835,plain,
% 1.34/1.59 (((~b(s(s(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))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2836,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, 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(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2835])).
% 1.34/1.59 tff(2837,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, 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(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.34/1.59 tff(2838,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2839,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.34/1.59 tff(2840,plain,
% 1.34/1.59 ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2839, 337, 327, 2813, 1591])).
% 1.34/1.59 tff(2841,plain,
% 1.34/1.59 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2840, 2811])).
% 1.34/1.59 tff(2842,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.59 tff(2843,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2844,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2845,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 1.34/1.59 tff(2846,plain,
% 1.34/1.59 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2845, 43, 2842, 2841])).
% 1.34/1.59 tff(2847,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2848,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2849,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 1.34/1.59 tff(2850,plain,
% 1.34/1.59 (~r(s(s(z)), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2849, 189, 2846, 2833])).
% 1.34/1.59 tff(2851,plain,
% 1.34/1.59 (b(s(s(z)), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2301, 2850, 2774])).
% 1.34/1.59 tff(2852,plain,
% 1.34/1.59 (~r(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1355, 189, 2783, 2833])).
% 1.34/1.59 tff(2853,plain,
% 1.34/1.59 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1360, 43])).
% 1.34/1.59 tff(2854,plain,
% 1.34/1.59 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2853, 2009])).
% 1.34/1.59 tff(2855,plain,
% 1.34/1.59 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2854, 2852])).
% 1.34/1.59 tff(2856,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.34/1.59 tff(2857,plain,
% 1.34/1.59 (~r(s(s(s(z))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1766, 189, 173, 118])).
% 1.34/1.59 tff(2858,plain,
% 1.34/1.59 (b(s(s(s(z))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1498, 2857])).
% 1.34/1.59 tff(2859,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2860,plain,
% 1.34/1.59 (((~b(s(s(s(z))), z)) | (~b(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(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2861,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2860])).
% 1.34/1.59 tff(2862,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2861, 2859])).
% 1.34/1.59 tff(2863,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(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)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2864,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.34/1.59 tff(2865,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2864, 337, 1274, 2858, 2856, 201])).
% 1.34/1.59 tff(2866,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2867,plain,
% 1.34/1.59 (~b(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2866, 2855, 118, 173])).
% 1.34/1.59 tff(2868,plain,
% 1.34/1.59 (r(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2242, 2867])).
% 1.34/1.59 tff(2869,plain,
% 1.34/1.59 (~r(s(s(z)), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2253, 2868, 173])).
% 1.34/1.59 tff(2870,plain,
% 1.34/1.59 (b(s(s(z)), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2229, 2869])).
% 1.34/1.59 tff(2871,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2872,plain,
% 1.34/1.60 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2873,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2872])).
% 1.34/1.60 tff(2874,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.60 inference(transitivity,[status(thm)],[2873, 2871])).
% 1.34/1.60 tff(2875,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(2876,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.34/1.60 tff(2877,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2876, 337, 327, 2775, 2870, 2851])).
% 1.34/1.60 tff(2878,plain,((~r(z, elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(elem!1), elem!1) | (s(z) = elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(2879,plain,
% 1.34/1.60 (~r(z, elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2878, 266, 173, 118, 2761, 2756, 83, 1169, 327, 2754, 1077])).
% 1.34/1.60 tff(2880,plain,
% 1.34/1.60 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 1.34/1.60 inference(monotonicity,[status(thm)],[251])).
% 1.34/1.60 tff(2881,plain,
% 1.34/1.60 (r(z, elem!1) <=> r(z, s(elem!1))),
% 1.34/1.60 inference(symmetry,[status(thm)],[2880])).
% 1.34/1.60 tff(2882,plain,
% 1.34/1.60 ((~r(z, elem!1)) <=> (~r(z, s(elem!1)))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2881])).
% 1.34/1.60 tff(2883,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.34/1.60 tff(2884,plain,
% 1.34/1.60 (~r(z, s(elem!1))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.34/1.60 tff(2885,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1077, 2884])).
% 1.34/1.60 tff(2886,plain,((~(s(elem!1) = elem!1)) | (~r(z, s(elem!1))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(2887,plain,
% 1.34/1.60 (~(s(elem!1) = elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2886, 2879, 1077])).
% 1.34/1.60 tff(2888,plain,
% 1.34/1.60 (~(elem!1 = s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[980, 2887])).
% 1.34/1.60 tff(2889,plain,
% 1.34/1.60 (~b(s(z), elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2578, 2888, 173, 1077, 50, 274, 327])).
% 1.34/1.60 tff(2890,plain,
% 1.34/1.60 (r(s(z), elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[727, 2889, 2754])).
% 1.34/1.60 tff(2891,plain,
% 1.34/1.60 (r(s(elem!1), elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[270, 2887, 266])).
% 1.34/1.60 tff(2892,plain,
% 1.34/1.60 (~r(s(z), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2129, 189, 2891, 2890])).
% 1.44/1.60 tff(2893,plain,
% 1.44/1.60 (~r(elem!1, s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1032, 274, 1077])).
% 1.44/1.60 tff(2894,plain,
% 1.44/1.60 (b(elem!1, s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1015, 2888, 2893])).
% 1.44/1.60 tff(2895,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[416, 189, 274, 1735, 275])).
% 1.44/1.60 tff(2896,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2897,plain,
% 1.44/1.60 (~r(s(z), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2896, 2890, 274])).
% 1.44/1.60 tff(2898,plain,
% 1.44/1.60 (b(s(z), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[963, 2897])).
% 1.44/1.60 tff(2899,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2900,plain,
% 1.44/1.60 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2901,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2900])).
% 1.44/1.60 tff(2902,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2901, 2899])).
% 1.44/1.60 tff(2903,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2904,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 1.44/1.60 tff(2905,plain,
% 1.44/1.60 (~b(s(z), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2904, 337, 327, 1544, 2898, 2894])).
% 1.44/1.60 tff(2906,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2133, 43, 2905, 2892, 55])).
% 1.44/1.60 tff(2907,plain,(b(s(elem!1), elem!1) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~r(elem!1, z)) | (s(z) = elem!1) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2908,plain,
% 1.44/1.60 (b(s(elem!1), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2907, 1711, 1544, 274, 272, 173, 1077, 50, 118, 83, 1169])).
% 1.44/1.60 tff(2909,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[83])).
% 1.44/1.60 tff(2910,plain,
% 1.44/1.60 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(symmetry,[status(thm)],[2909])).
% 1.44/1.60 tff(2911,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2520, 2910])).
% 1.44/1.60 tff(2912,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[984, 2911])).
% 1.44/1.60 tff(2913,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2914,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2913, 2908, 83])).
% 1.44/1.60 tff(2915,plain,
% 1.44/1.60 (r(s(z), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2594, 2908, 247, 1544, 1710])).
% 1.44/1.60 tff(2916,plain,
% 1.44/1.60 (~r(z, elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1743, 2915, 173])).
% 1.44/1.60 tff(2917,plain,
% 1.44/1.60 (b(z, elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[921, 2916, 61])).
% 1.44/1.60 tff(2918,plain,
% 1.44/1.60 (~b(elem!1, s(s(s(elem!1))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[972, 2917, 2914, 1711])).
% 1.44/1.60 tff(2919,plain,
% 1.44/1.60 (~b(elem!1, s(elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2918, 2753])).
% 1.44/1.60 tff(2920,plain,
% 1.44/1.60 (~(s(elem!1) = elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2886, 2916, 1077])).
% 1.44/1.60 tff(2921,plain,
% 1.44/1.60 (~(elem!1 = s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[980, 2920])).
% 1.44/1.60 tff(2922,plain,
% 1.44/1.60 (b(elem!1, s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1015, 2921, 2893])).
% 1.44/1.60 tff(2923,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2922, 2919])).
% 1.44/1.60 tff(2924,plain,((~r(elem!1, z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (elem!1 = s(z)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2925,plain,
% 1.44/1.60 (~r(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2924, 2734, 2751, 173, 244, 2749, 50, 118, 2747])).
% 1.44/1.60 tff(2926,plain,
% 1.44/1.60 (b(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1759, 2925, 68])).
% 1.44/1.60 tff(2927,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2928,plain,
% 1.44/1.60 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2929,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2928])).
% 1.44/1.60 tff(2930,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2929, 2927])).
% 1.44/1.60 tff(2931,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2932,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2931, 2930])).
% 1.44/1.60 tff(2933,plain,
% 1.44/1.60 (~b(s(s(s(z))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2932, 337, 2926, 1770, 201])).
% 1.44/1.60 tff(2934,plain,
% 1.44/1.60 (r(s(s(s(z))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2463, 2933, 2745])).
% 1.44/1.60 tff(2935,plain,
% 1.44/1.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1812, 189, 2747, 2934])).
% 1.44/1.60 tff(2936,plain,
% 1.44/1.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[548, 2935])).
% 1.44/1.60 tff(2937,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2938,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2939,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 1.44/1.60 tff(2940,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2939, 189, 2747, 2934])).
% 1.44/1.60 tff(2941,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[524, 2940])).
% 1.44/1.60 tff(2942,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2943,plain,
% 1.44/1.60 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, 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))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2944,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, 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))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2943])).
% 1.44/1.60 tff(2945,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, 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))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2944, 2942])).
% 1.44/1.60 tff(2946,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, 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))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2947,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.44/1.60 tff(2948,plain,
% 1.44/1.60 (~b(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2947, 337, 2941, 2936, 201])).
% 1.44/1.60 tff(2949,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1792, 2948])).
% 1.44/1.60 tff(2950,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2023, 2949, 173])).
% 1.44/1.60 tff(2951,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[851, 2950])).
% 1.44/1.60 tff(2952,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2953,plain,
% 1.44/1.60 (((~b(s(s(s(s(z)))), 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(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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2954,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2953])).
% 1.44/1.60 tff(2955,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2954, 2952])).
% 1.44/1.60 tff(2956,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2957,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.44/1.60 tff(2958,plain,
% 1.44/1.60 (~b(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2957, 337, 2941, 2936, 201])).
% 1.44/1.60 tff(2959,plain,
% 1.44/1.60 (r(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1786, 2958])).
% 1.44/1.60 tff(2960,plain,
% 1.44/1.60 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1580, 2959, 173])).
% 1.44/1.60 tff(2961,plain,
% 1.44/1.60 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1150, 2960])).
% 1.44/1.60 tff(2962,plain,
% 1.44/1.60 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2107, 337, 2749, 2961, 2951])).
% 1.44/1.60 tff(2963,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[832, 43, 2744, 2962])).
% 1.44/1.60 tff(2964,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2965,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2966,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2965, 2964])).
% 1.44/1.60 tff(2967,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2966, 189, 2751, 2949, 2963])).
% 1.44/1.60 tff(2968,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2969,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2968, 81, 118, 50, 82])).
% 1.44/1.60 tff(2970,plain,
% 1.44/1.60 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[223, 81, 147])).
% 1.44/1.60 tff(2971,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[227, 43, 2970, 213])).
% 1.44/1.60 tff(2972,plain,
% 1.44/1.60 (~(elem!1 = s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[935, 925, 69])).
% 1.44/1.60 tff(2973,plain,
% 1.44/1.60 (~r(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1754, 2972, 82, 81, 50, 172, 273])).
% 1.44/1.60 tff(2974,plain,
% 1.44/1.60 (b(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1759, 2973, 68])).
% 1.44/1.60 tff(2975,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2976,plain,
% 1.44/1.60 (((~b(z, elem!1)) | (~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)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2977,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2976])).
% 1.44/1.61 tff(2978,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2977, 2975])).
% 1.44/1.61 tff(2979,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2980,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 1.44/1.61 tff(2981,plain,
% 1.44/1.61 (~b(s(s(s(s(z)))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2980, 337, 925, 2974, 1603])).
% 1.44/1.61 tff(2982,plain,
% 1.44/1.61 (r(s(s(s(s(z)))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1792, 2981])).
% 1.44/1.61 tff(2983,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2023, 2982, 81])).
% 1.44/1.61 tff(2984,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[851, 2983])).
% 1.44/1.61 tff(2985,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2986,plain,
% 1.44/1.61 (((~b(z, elem!1)) | (~b(s(s(s(s(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2987,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(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(X1, 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(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2986])).
% 1.44/1.61 tff(2988,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(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(X1, 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(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2987, 2985])).
% 1.44/1.61 tff(2989,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(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)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2990,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2989, 2988])).
% 1.44/1.61 tff(2991,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2990, 337, 925, 1763, 1603, 1592])).
% 1.44/1.61 tff(2992,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,[]))).
% 1.44/1.61 tff(2993,plain,
% 1.44/1.61 (~b(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2992, 2974, 1603, 925])).
% 1.44/1.61 tff(2994,plain,
% 1.44/1.61 (r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1786, 2993])).
% 1.44/1.61 tff(2995,plain,
% 1.44/1.61 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1580, 2994, 81])).
% 1.44/1.61 tff(2996,plain,
% 1.44/1.61 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1150, 2995])).
% 1.44/1.61 tff(2997,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2998,plain,
% 1.44/1.61 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), 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(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))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2999,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2998])).
% 1.44/1.61 tff(3000,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2999, 2997])).
% 1.44/1.61 tff(3001,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3002,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3001, 3000])).
% 1.44/1.61 tff(3003,plain,
% 1.44/1.61 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3002, 337, 2996, 2984, 2971])).
% 1.44/1.61 tff(3004,plain,
% 1.44/1.61 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1943, 2972])).
% 1.44/1.61 tff(3005,plain,
% 1.44/1.61 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1947, 43, 3004, 3003])).
% 1.44/1.61 tff(3006,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3007,plain,
% 1.44/1.61 (((~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))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3008,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3007])).
% 1.44/1.61 tff(3009,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3008, 3006])).
% 1.44/1.61 tff(3010,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3011,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 1.44/1.61 tff(3012,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3011, 189, 147, 2982, 3005])).
% 1.44/1.61 tff(3013,plain,((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | b(z, s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3014,plain,
% 1.44/1.61 (~b(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3013, 271, 82, 50, 172, 2969, 69])).
% 1.44/1.61 tff(3015,plain,
% 1.44/1.61 (r(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[921, 3014, 61])).
% 1.44/1.61 tff(3016,plain,
% 1.44/1.61 (~r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[785, 3015, 81])).
% 1.44/1.61 tff(3017,plain,
% 1.44/1.61 (~r(s(z), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1743, 3015, 81])).
% 1.44/1.61 tff(3018,plain,
% 1.44/1.61 (elem!1 = s(z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2031, 3017, 118, 81, 2969, 3016])).
% 1.44/1.61 tff(3019,plain,
% 1.44/1.61 (b(elem!1, z) <=> b(s(z), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3018])).
% 1.44/1.61 tff(3020,plain,
% 1.44/1.61 (b(s(z), z) <=> b(elem!1, z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[3019])).
% 1.44/1.61 tff(3021,plain,
% 1.44/1.61 (~b(elem!1, z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2045, 3015, 118, 50, 81, 266, 147])).
% 1.44/1.61 tff(3022,plain,
% 1.44/1.61 (r(elem!1, z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1759, 3021, 68])).
% 1.44/1.61 tff(3023,plain,
% 1.44/1.61 (~r(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1699, 3022, 82, 172, 50, 271])).
% 1.44/1.61 tff(3024,plain,
% 1.44/1.61 (b(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[963, 3023])).
% 1.44/1.61 tff(3025,plain,
% 1.44/1.61 (b(elem!1, z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3024, 3020])).
% 1.44/1.61 tff(3026,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3021, 3025])).
% 1.44/1.61 tff(3027,plain,(b(s(elem!1), elem!1) | b(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3028,plain,
% 1.44/1.61 (b(s(elem!1), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3027, 172, 82, 50, 118, 69])).
% 1.44/1.61 tff(3029,plain,
% 1.44/1.61 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1188])).
% 1.44/1.61 tff(3030,plain,
% 1.44/1.61 (~b(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[935, 230, 69])).
% 1.44/1.61 tff(3031,plain,
% 1.44/1.61 (r(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[921, 3030, 65])).
% 1.44/1.61 tff(3032,plain,
% 1.44/1.61 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[232, 230])).
% 1.44/1.61 tff(3033,plain,
% 1.44/1.61 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[3032])).
% 1.44/1.61 tff(3034,plain,
% 1.44/1.61 (r(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[118, 3033])).
% 1.44/1.61 tff(3035,plain,
% 1.44/1.61 (~r(s(elem!1), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2010, 3034, 1273, 3031])).
% 1.44/1.61 tff(3036,plain,
% 1.44/1.61 (~r(s(elem!1), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3035, 3029])).
% 1.44/1.61 tff(3037,plain,
% 1.44/1.61 (~r(s(z), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1743, 3031, 81])).
% 1.44/1.61 tff(3038,plain,
% 1.44/1.61 (~r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[785, 3031, 81])).
% 1.44/1.61 tff(3039,plain,
% 1.44/1.61 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[231])).
% 1.44/1.61 tff(3040,plain,
% 1.44/1.61 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.61 tff(3041,plain,
% 1.44/1.61 (b(s(elem!1), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2520, 3040])).
% 1.44/1.61 tff(3042,plain,
% 1.44/1.61 (b(s(s(z)), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3041, 3039])).
% 1.44/1.61 tff(3043,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1603, 237])).
% 1.44/1.61 tff(3044,plain,
% 1.44/1.61 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.61 tff(3045,plain,
% 1.44/1.61 (r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[215, 3044])).
% 1.44/1.61 tff(3046,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1783, 3045])).
% 1.44/1.61 tff(3047,plain,((~r(z, s(s(s(elem!1))))) | r(z, s(s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3048,plain,
% 1.44/1.61 (r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3047, 230, 215])).
% 1.44/1.61 tff(3049,plain,
% 1.44/1.61 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1580, 3048, 81])).
% 1.44/1.61 tff(3050,plain,
% 1.44/1.61 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1150, 3049])).
% 1.44/1.61 tff(3051,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3052,plain,
% 1.44/1.61 (((~b(s(s(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(z))) | (~b(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))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3053,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3052])).
% 1.44/1.61 tff(3054,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3053, 3051])).
% 1.44/1.61 tff(3055,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3056,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 1.44/1.61 tff(3057,plain,
% 1.44/1.61 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3056, 337, 3050, 3043, 3042])).
% 1.44/1.61 tff(3058,plain,
% 1.44/1.61 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1133, 3057, 230])).
% 1.44/1.61 tff(3059,plain,
% 1.44/1.61 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[579, 3058, 428])).
% 1.44/1.61 tff(3060,plain,
% 1.44/1.61 (~r(s(elem!1), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1227, 3059, 215])).
% 1.44/1.61 tff(3061,plain,
% 1.44/1.61 (b(s(elem!1), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1262, 3060, 230])).
% 1.44/1.61 tff(3062,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.44/1.61 tff(3063,plain,
% 1.44/1.61 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[56])).
% 1.44/1.61 tff(3064,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3063])).
% 1.44/1.61 tff(3065,plain,
% 1.44/1.61 ((~r(elem!1, s(z))) <=> (~r(z, s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3064])).
% 1.44/1.61 tff(3066,plain,
% 1.44/1.61 (~r(z, s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1075, 3065])).
% 1.44/1.61 tff(3067,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[173, 3066])).
% 1.44/1.61 tff(3068,plain,((~(z = elem!1)) | (~r(z, s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3069,plain,
% 1.44/1.61 (~(z = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3068, 1075, 173])).
% 1.44/1.61 tff(3070,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.44/1.61 tff(3071,plain,
% 1.44/1.61 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3070])).
% 1.44/1.61 tff(3072,plain,
% 1.44/1.61 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3071])).
% 1.44/1.61 tff(3073,plain,
% 1.44/1.61 (z = inj_0(s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[14])).
% 1.44/1.61 tff(3074,plain,
% 1.44/1.61 (z = elem!1),
% 1.44/1.61 inference(transitivity,[status(thm)],[3073, 3072, 91])).
% 1.44/1.61 tff(3075,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[65, 3074])).
% 1.44/1.61 tff(3076,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3077,plain,
% 1.44/1.61 (~(s(elem!1) = s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3076, 3069])).
% 1.44/1.61 tff(3078,plain,
% 1.44/1.61 (b(s(elem!1), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[898, 3077, 1871])).
% 1.44/1.61 tff(3079,plain,
% 1.44/1.61 (b(s(elem!1), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[270, 3062, 265])).
% 1.44/1.61 tff(3080,plain,
% 1.44/1.61 (elem!1 = s(z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2594, 3078, 3079, 1878, 1075])).
% 1.44/1.61 tff(3081,plain,
% 1.44/1.61 (~(s(s(s(z))) = s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[452, 3080, 3077])).
% 1.44/1.61 tff(3082,plain,
% 1.44/1.61 (~(elem!1 = z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[67, 3069])).
% 1.44/1.61 tff(3083,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.44/1.61 tff(3084,plain,
% 1.44/1.61 (s(s(z)) = s(z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[3083])).
% 1.44/1.61 tff(3085,plain,
% 1.44/1.61 (s(elem!1) = s(z)),
% 1.44/1.61 inference(transitivity,[status(thm)],[231, 3084])).
% 1.44/1.61 tff(3086,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[50, 3085])).
% 1.44/1.61 tff(3087,plain,((~(s(z) = s(s(z)))) | (s(elem!1) = s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3088,plain,
% 1.44/1.61 (~(s(z) = s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3087, 3077, 3080])).
% 1.44/1.61 tff(3089,plain,
% 1.44/1.61 (s(elem!1) = s(s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3080])).
% 1.44/1.61 tff(3090,plain,
% 1.44/1.61 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3089])).
% 1.44/1.61 tff(3091,plain,
% 1.44/1.61 (b(s(s(z)), z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[599, 3090])).
% 1.44/1.61 tff(3092,plain,
% 1.44/1.61 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1102])).
% 1.44/1.61 tff(3093,plain,
% 1.44/1.61 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3092])).
% 1.44/1.61 tff(3094,plain,
% 1.44/1.61 (b(s(s(z)), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1544, 3093])).
% 1.44/1.61 tff(3095,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.61 tff(3096,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3095, 3094])).
% 1.44/1.61 tff(3097,plain,(b(s(s(z)), s(z)) | (~b(s(elem!1), s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3098,plain,
% 1.44/1.61 (b(s(s(z)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3097, 1544, 230])).
% 1.44/1.61 tff(3099,assumption,(~(s(z) = s(s(z)))), introduced(assumption)).
% 1.44/1.61 tff(3100,plain,
% 1.44/1.61 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[231])).
% 1.44/1.61 tff(3101,plain,
% 1.44/1.61 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3100])).
% 1.44/1.61 tff(3102,plain,
% 1.44/1.61 ((~b(z, s(s(z)))) <=> (~b(z, s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3101])).
% 1.44/1.61 tff(3103,plain,
% 1.44/1.61 (b(elem!1, z) <=> b(s(z), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.61 tff(3104,plain,
% 1.44/1.61 (r(s(s(s(s(z)))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1792, 1790])).
% 1.44/1.61 tff(3105,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2023, 3104, 173])).
% 1.44/1.61 tff(3106,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[851, 3105])).
% 1.44/1.61 tff(3107,plain,
% 1.44/1.61 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.61 tff(3108,plain,
% 1.44/1.61 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3107])).
% 1.44/1.61 tff(3109,plain,
% 1.44/1.61 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.61 tff(3110,plain,
% 1.44/1.61 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[3109])).
% 1.44/1.61 tff(3111,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.61 tff(3112,plain,
% 1.44/1.61 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3111])).
% 1.44/1.61 tff(3113,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.61 tff(3114,plain,
% 1.44/1.61 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3113])).
% 1.44/1.61 tff(3115,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.61 tff(3116,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3115, 681])).
% 1.44/1.61 tff(3117,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3116, 682])).
% 1.44/1.61 tff(3118,plain,
% 1.44/1.61 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3117])).
% 1.44/1.61 tff(3119,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.62 tff(3120,plain,
% 1.44/1.62 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3119])).
% 1.44/1.62 tff(3121,plain,
% 1.44/1.62 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3120])).
% 1.44/1.62 tff(3122,plain,
% 1.44/1.62 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[121, 3121, 98])).
% 1.44/1.62 tff(3123,plain,
% 1.44/1.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3122])).
% 1.44/1.62 tff(3124,plain,
% 1.44/1.62 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3123])).
% 1.44/1.62 tff(3125,plain,
% 1.44/1.62 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3121])).
% 1.44/1.62 tff(3126,plain,
% 1.44/1.62 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.62 inference(transitivity,[status(thm)],[130, 3125, 3124, 110])).
% 1.44/1.62 tff(3127,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[172, 3126])).
% 1.44/1.62 tff(3128,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3129,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3128, 172])).
% 1.44/1.62 tff(3130,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3129, 3118])).
% 1.44/1.62 tff(3131,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.62 tff(3132,plain,
% 1.44/1.62 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3131])).
% 1.44/1.62 tff(3133,plain,
% 1.44/1.62 (r(elem!1, z) <=> r(s(z), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.62 tff(3134,plain,
% 1.44/1.62 (r(s(z), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[274, 3133])).
% 1.44/1.62 tff(3135,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.62 tff(3136,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[3135])).
% 1.44/1.62 tff(3137,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(transitivity,[status(thm)],[235, 3136])).
% 1.44/1.62 tff(3138,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1231, 3137])).
% 1.44/1.62 tff(3139,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.62 tff(3140,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(symmetry,[status(thm)],[3139])).
% 1.44/1.62 tff(3141,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[820, 43, 817, 1790])).
% 1.44/1.62 tff(3142,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3141, 3140])).
% 1.44/1.62 tff(3143,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.44/1.62 tff(3144,plain,
% 1.44/1.62 (r(z, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[395, 3143])).
% 1.44/1.62 tff(3145,plain,
% 1.44/1.62 (~r(elem!1, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1032, 3144, 274])).
% 1.44/1.62 tff(3146,plain,
% 1.44/1.62 (~(elem!1 = s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[980, 978])).
% 1.44/1.62 tff(3147,plain,
% 1.44/1.62 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1013, 43, 1010])).
% 1.44/1.62 tff(3148,plain,
% 1.44/1.62 (b(elem!1, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3147, 3146])).
% 1.44/1.62 tff(3149,plain,
% 1.44/1.62 (b(s(elem!1), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[270, 978, 3062])).
% 1.44/1.62 tff(3150,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3151,plain,
% 1.44/1.62 (((~b(s(elem!1), elem!1)) | (~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(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3152,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3151])).
% 1.44/1.62 tff(3153,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3152, 3150])).
% 1.44/1.62 tff(3154,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3155,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.44/1.62 tff(3156,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3155, 337, 365, 326, 3149, 3148])).
% 1.44/1.62 tff(3157,plain,((s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3158,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3157, 3145, 3062, 326, 265])).
% 1.44/1.62 tff(3159,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[363, 3158, 172])).
% 1.44/1.62 tff(3160,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3161,plain,
% 1.44/1.62 (((~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))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3162,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3161])).
% 1.44/1.62 tff(3163,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3162, 3160])).
% 1.44/1.62 tff(3164,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3165,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 1.44/1.62 tff(3166,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3165, 189, 353, 1077, 2177])).
% 1.44/1.62 tff(3167,plain,((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3168,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3167, 3159, 3144])).
% 1.44/1.62 tff(3169,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3168, 3142])).
% 1.44/1.62 tff(3170,plain,(b(z, s(elem!1)) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3171,plain,
% 1.44/1.62 (b(z, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3170, 1790, 172, 3062, 3138, 274, 230])).
% 1.44/1.62 tff(3172,plain,
% 1.44/1.62 (b(z, s(s(z)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3171, 3100])).
% 1.44/1.62 tff(3173,plain,
% 1.44/1.62 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1102])).
% 1.44/1.62 tff(3174,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3173])).
% 1.44/1.62 tff(3175,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.62 tff(3176,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3177,plain,
% 1.44/1.62 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3178,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3177])).
% 1.44/1.62 tff(3179,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3178, 3176])).
% 1.44/1.62 tff(3180,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3181,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3180, 3179])).
% 1.44/1.62 tff(3182,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3181, 189, 275, 3141])).
% 1.44/1.62 tff(3183,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1150, 3182])).
% 1.44/1.62 tff(3184,plain,
% 1.44/1.62 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3056, 337, 3183, 1231, 3094])).
% 1.44/1.62 tff(3185,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1133, 3184, 230])).
% 1.44/1.62 tff(3186,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[579, 3185, 983])).
% 1.44/1.62 tff(3187,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3186, 3175])).
% 1.44/1.62 tff(3188,plain,
% 1.44/1.62 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3187, 3174])).
% 1.44/1.62 tff(3189,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1356, 3188])).
% 1.44/1.62 tff(3190,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1360, 43, 458, 3189])).
% 1.44/1.62 tff(3191,plain,
% 1.44/1.62 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3192,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3191])).
% 1.44/1.62 tff(3193,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3192, 1343])).
% 1.44/1.62 tff(3194,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3195,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3194, 3193])).
% 1.44/1.62 tff(3196,plain,
% 1.44/1.62 (~b(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3195, 337, 1274, 1342, 3190])).
% 1.44/1.62 tff(3197,plain,
% 1.44/1.62 (r(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1498, 3196])).
% 1.44/1.62 tff(3198,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3199,plain,
% 1.44/1.62 (((~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(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3200,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3199])).
% 1.44/1.62 tff(3201,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3200, 3198])).
% 1.44/1.62 tff(3202,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3203,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3202, 3201])).
% 1.44/1.62 tff(3204,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3203, 189, 1339, 3197, 3141])).
% 1.44/1.62 tff(3205,plain,((~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(s(z))) = s(s(z))) | (~(elem!1 = s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | b(s(s(s(s(z)))), z) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3206,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3205, 3172, 1274, 458, 230, 428, 1231, 3134, 1790, 1544])).
% 1.44/1.62 tff(3207,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[548, 3206])).
% 1.44/1.62 tff(3208,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3181, 189, 3134, 3141])).
% 1.44/1.62 tff(3209,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1150, 3208])).
% 1.44/1.62 tff(3210,plain,
% 1.44/1.62 (~b(s(s(s(z))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1281, 337, 3209, 3207, 1231])).
% 1.44/1.62 tff(3211,plain,
% 1.44/1.62 (r(s(s(s(z))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[48, 3210])).
% 1.44/1.62 tff(3212,plain,
% 1.44/1.62 (~r(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1766, 189, 173, 3211])).
% 1.44/1.62 tff(3213,plain,
% 1.44/1.62 (b(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1498, 3212])).
% 1.44/1.62 tff(3214,plain,
% 1.44/1.62 (~b(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1348, 337, 1274, 3172, 3213])).
% 1.44/1.62 tff(3215,plain,
% 1.44/1.62 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1360, 43, 458, 3214])).
% 1.44/1.62 tff(3216,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[233, 231])).
% 1.44/1.62 tff(3217,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1231, 235])).
% 1.44/1.62 tff(3218,plain,
% 1.44/1.62 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.62 tff(3219,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3218])).
% 1.44/1.62 tff(3220,plain,
% 1.44/1.62 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3209, 3219])).
% 1.44/1.62 tff(3221,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2144, 3220, 1544, 3217])).
% 1.44/1.62 tff(3222,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[363, 3221, 172])).
% 1.44/1.62 tff(3223,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3222, 3216])).
% 1.44/1.62 tff(3224,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3225,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3226,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 1.44/1.62 tff(3227,plain,
% 1.44/1.62 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3226, 189, 3223, 3215])).
% 1.44/1.62 tff(3228,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[524, 3227])).
% 1.44/1.62 tff(3229,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3230,plain,
% 1.44/1.62 (((~b(s(s(z)), z)) | (~b(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3231,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3230])).
% 1.44/1.62 tff(3232,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3231, 3229])).
% 1.44/1.62 tff(3233,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3234,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 1.44/1.62 tff(3235,plain,
% 1.44/1.62 (~b(s(s(z)), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3234, 337, 1274, 3172, 3213])).
% 1.44/1.62 tff(3236,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1298, 43, 3235])).
% 1.44/1.62 tff(3237,plain,
% 1.44/1.62 (r(s(s(z)), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3236, 1286])).
% 1.44/1.62 tff(3238,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.62 tff(3239,plain,
% 1.44/1.62 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3238])).
% 1.44/1.62 tff(3240,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3108])).
% 1.44/1.62 tff(3241,plain,
% 1.44/1.62 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3240])).
% 1.44/1.62 tff(3242,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.62 tff(3243,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(3244,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), 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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3245,plain,
% 1.44/1.63 (((~b(s(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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3246,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3245])).
% 1.44/1.63 tff(3247,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3246, 3244])).
% 1.44/1.63 tff(3248,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3249,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 1.44/1.63 tff(3250,plain,
% 1.44/1.63 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3249, 337, 3243, 2, 3242])).
% 1.44/1.63 tff(3251,plain,
% 1.44/1.63 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3250, 3241])).
% 1.44/1.63 tff(3252,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[612, 1913])).
% 1.44/1.63 tff(3253,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3252, 3251])).
% 1.44/1.63 tff(3254,plain,
% 1.44/1.63 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3253, 3239])).
% 1.44/1.63 tff(3255,plain,
% 1.44/1.63 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[635, 1273])).
% 1.44/1.63 tff(3256,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(3257,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1268])).
% 1.44/1.63 tff(3258,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3257, 3256])).
% 1.44/1.63 tff(3259,plain,
% 1.44/1.63 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3258])).
% 1.44/1.63 tff(3260,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[135, 3259])).
% 1.44/1.63 tff(3261,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1268, 3108])).
% 1.44/1.63 tff(3262,plain,
% 1.44/1.63 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3261])).
% 1.44/1.63 tff(3263,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(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(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3264,plain,
% 1.44/1.63 (((~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(z)))), s(z))) | (~b(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(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3265,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3264])).
% 1.44/1.63 tff(3266,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3265, 3263])).
% 1.44/1.63 tff(3267,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(z))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3268,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 1.44/1.63 tff(3269,plain,
% 1.44/1.63 (~b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3268, 337, 1275, 1231, 3242])).
% 1.44/1.63 tff(3270,plain,
% 1.44/1.63 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3269, 3262])).
% 1.44/1.63 tff(3271,plain,
% 1.44/1.63 (((~![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))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3272,plain,
% 1.44/1.63 ((~![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))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3273,plain,
% 1.44/1.63 ((~![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)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.44/1.63 tff(3274,plain,
% 1.44/1.63 ((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)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3273, 43])).
% 1.44/1.63 tff(3275,plain,
% 1.44/1.63 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3274, 3270, 3260])).
% 1.44/1.63 tff(3276,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.44/1.63 tff(3277,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.63 tff(3278,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3279,plain,
% 1.44/1.63 (((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3280,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3279])).
% 1.44/1.63 tff(3281,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3280, 3278])).
% 1.44/1.63 tff(3282,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3283,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.44/1.63 tff(3284,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3283, 189, 274, 3277, 3276])).
% 1.44/1.63 tff(3285,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(3286,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3285, 3275, 274])).
% 1.44/1.63 tff(3287,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[663, 3286])).
% 1.44/1.63 tff(3288,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3287, 3110])).
% 1.44/1.63 tff(3289,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3290,plain,
% 1.44/1.63 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3291,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3290])).
% 1.44/1.63 tff(3292,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3291, 3289])).
% 1.44/1.63 tff(3293,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3294,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3293, 3292])).
% 1.44/1.63 tff(3295,plain,
% 1.44/1.63 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3294, 337, 1274, 1342, 3288])).
% 1.44/1.63 tff(3296,plain,
% 1.44/1.63 (((~![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)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3297,plain,
% 1.44/1.63 ((~![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)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3298,plain,
% 1.44/1.63 ((~![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))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3297, 3296])).
% 1.44/1.63 tff(3299,plain,
% 1.44/1.63 ((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))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3298, 43])).
% 1.44/1.63 tff(3300,plain,
% 1.44/1.63 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3299, 3295, 3255])).
% 1.44/1.63 tff(3301,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.63 tff(3302,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3303,plain,
% 1.44/1.63 (((~r(s(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(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3304,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3303])).
% 1.44/1.63 tff(3305,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3304, 3302])).
% 1.44/1.63 tff(3306,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3307,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3306, 3305])).
% 1.44/1.63 tff(3308,plain,
% 1.44/1.63 ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3307, 189, 3301])).
% 1.44/1.63 tff(3309,plain,
% 1.44/1.63 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3308, 3300])).
% 1.44/1.63 tff(3310,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3309, 3254])).
% 1.44/1.63 tff(3311,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(3312,plain,
% 1.44/1.63 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3311, 3237, 230, 1274, 3172, 274, 3209, 1231, 3228, 3207])).
% 1.44/1.63 tff(3313,plain,
% 1.44/1.63 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3312, 3132])).
% 1.44/1.63 tff(3314,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[700, 3313, 3130])).
% 1.44/1.63 tff(3315,plain,
% 1.44/1.63 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3314, 3114])).
% 1.44/1.63 tff(3316,plain,
% 1.44/1.63 (~r(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[195, 189, 173, 3211])).
% 1.44/1.63 tff(3317,plain,
% 1.44/1.63 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[199, 43, 3316])).
% 1.44/1.63 tff(3318,plain,
% 1.44/1.63 (b(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3317, 179])).
% 1.44/1.63 tff(3319,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3320,plain,
% 1.44/1.63 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3321,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3320])).
% 1.44/1.63 tff(3322,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3321, 3319])).
% 1.44/1.63 tff(3323,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3324,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 1.44/1.63 tff(3325,plain,
% 1.44/1.63 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3324, 337, 3207, 1231, 3318])).
% 1.44/1.63 tff(3326,plain,
% 1.44/1.63 (~b(z, s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3325, 3228])).
% 1.44/1.63 tff(3327,plain,
% 1.44/1.63 (r(z, s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1584, 43, 3326, 1562])).
% 1.44/1.63 tff(3328,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3329,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), z)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3330,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))), z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 1.44/1.63 tff(3331,plain,
% 1.44/1.63 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3330, 189, 3327])).
% 1.44/1.63 tff(3332,plain,
% 1.44/1.63 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3331, 3315])).
% 1.44/1.63 tff(3333,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3332, 3112])).
% 1.44/1.63 tff(3334,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[663, 3333])).
% 1.44/1.63 tff(3335,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3334, 3110])).
% 1.44/1.64 tff(3336,plain,
% 1.44/1.64 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3056, 337, 3209, 1231])).
% 1.44/1.64 tff(3337,plain,
% 1.44/1.64 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3336, 3094])).
% 1.44/1.64 tff(3338,plain,
% 1.44/1.64 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1133, 3337, 230])).
% 1.44/1.64 tff(3339,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[579, 3338, 428])).
% 1.44/1.64 tff(3340,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3339, 3175])).
% 1.44/1.64 tff(3341,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3340, 3174])).
% 1.44/1.64 tff(3342,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3343,plain,
% 1.44/1.64 (((~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(s(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)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3344,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3343])).
% 1.44/1.64 tff(3345,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3344, 3342])).
% 1.44/1.64 tff(3346,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3347,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.44/1.64 tff(3348,plain,
% 1.44/1.64 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3347, 189])).
% 1.44/1.64 tff(3349,plain,
% 1.44/1.64 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3348, 3315, 3341])).
% 1.44/1.64 tff(3350,plain,
% 1.44/1.64 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3299, 3349, 3255])).
% 1.44/1.64 tff(3351,plain,
% 1.44/1.64 (~b(s(s(s(s(s(z))))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3294, 337, 3350, 1274, 3172])).
% 1.44/1.64 tff(3352,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3351, 3335])).
% 1.44/1.64 tff(3353,plain,(b(s(s(s(s(z)))), z) | (~(elem!1 = s(z))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(z))) | (~r(z, s(z))) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3354,plain,
% 1.44/1.64 (~r(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3353, 3106, 1274, 230, 1790, 458, 173, 1544, 172, 3062])).
% 1.44/1.64 tff(3355,plain,
% 1.44/1.64 (b(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1759, 3354, 1900])).
% 1.44/1.64 tff(3356,plain,
% 1.44/1.64 (b(s(z), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3355, 3103])).
% 1.44/1.64 tff(3357,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.64 tff(3358,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3359,plain,
% 1.44/1.64 (((~b(s(s(z)), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3360,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3359])).
% 1.44/1.64 tff(3361,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3360, 3358])).
% 1.44/1.64 tff(3362,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3363,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.44/1.64 tff(3364,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3363, 337, 1, 1274, 1342, 3357])).
% 1.44/1.64 tff(3365,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3366,plain,
% 1.44/1.64 (~b(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3365, 3356, 1274, 3098])).
% 1.44/1.64 tff(3367,plain,
% 1.44/1.64 (~b(z, s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3366, 3102])).
% 1.44/1.64 tff(3368,plain,
% 1.44/1.64 (r(z, s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[395, 3367])).
% 1.44/1.64 tff(3369,plain,
% 1.44/1.64 (r(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1108, 3368, 230])).
% 1.44/1.64 tff(3370,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(3371,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3372,plain,
% 1.44/1.64 (((~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)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3373,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3372])).
% 1.44/1.64 tff(3374,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3373, 3371])).
% 1.44/1.64 tff(3375,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3376,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3375, 3374])).
% 1.44/1.64 tff(3377,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3376, 189, 173, 1116, 3370])).
% 1.44/1.64 tff(3378,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3379,plain,
% 1.44/1.64 (~r(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3378, 3369, 173])).
% 1.44/1.64 tff(3380,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(3381,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(3382,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3383,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3384,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3383, 3382])).
% 1.44/1.64 tff(3385,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3384, 43, 3381, 3099, 3380])).
% 1.44/1.64 tff(3386,plain,(b(s(z), s(s(z))) | (s(z) = s(s(z))) | r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3387,plain,
% 1.44/1.64 (b(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3386, 3379, 3099])).
% 1.44/1.64 tff(3388,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3389,plain,
% 1.44/1.64 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3390,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3389])).
% 1.44/1.64 tff(3391,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3390, 3388])).
% 1.44/1.64 tff(3392,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3393,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 1.44/1.64 tff(3394,plain,
% 1.44/1.64 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3393, 337, 3106, 3387, 3098])).
% 1.44/1.64 tff(3395,plain,
% 1.44/1.64 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1133, 3394, 230])).
% 1.44/1.64 tff(3396,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[579, 3395, 428])).
% 1.44/1.64 tff(3397,plain,
% 1.44/1.64 (~r(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1125, 3396, 230, 3369])).
% 1.44/1.64 tff(3398,plain,
% 1.44/1.64 (~r(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3047, 3397, 230])).
% 1.44/1.64 tff(3399,plain,
% 1.44/1.64 (b(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[146, 3398])).
% 1.44/1.64 tff(3400,plain,
% 1.44/1.64 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[233])).
% 1.44/1.64 tff(3401,plain,
% 1.44/1.64 (b(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1925, 3400])).
% 1.44/1.64 tff(3402,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1784, 3401])).
% 1.44/1.64 tff(3403,plain,((~b(z, s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3404,plain,
% 1.44/1.64 (b(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3403, 3399, 230])).
% 1.44/1.64 tff(3405,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3406,plain,
% 1.44/1.64 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), 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(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3407,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3406])).
% 1.44/1.64 tff(3408,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3407, 3405])).
% 1.44/1.64 tff(3409,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3410,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3409, 3408])).
% 1.44/1.64 tff(3411,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3410, 337, 3356, 3106, 3404, 3387, 1274, 3098])).
% 1.44/1.64 tff(3412,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(z)), z)) | (~(elem!1 = s(z))) | (s(z) = s(s(z))) | (~r(z, s(z))) | (elem!1 = z) | (s(s(s(z))) = s(s(z))) | (~b(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3413,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3412, 3091, 3080, 3088, 173, 3082, 3081, 3078, 172, 3062])).
% 1.44/1.64 tff(3414,plain,
% 1.44/1.64 (b(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3097, 3078, 3080])).
% 1.44/1.64 tff(3415,plain,
% 1.44/1.64 (~r(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3047, 1857, 230])).
% 1.44/1.64 tff(3416,plain,
% 1.44/1.64 (b(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[146, 3415])).
% 1.44/1.64 tff(3417,plain,
% 1.44/1.64 (b(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3403, 3416, 230])).
% 1.44/1.64 tff(3418,plain,
% 1.44/1.64 (~(s(s(s(z))) = s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[452, 230, 50])).
% 1.44/1.64 tff(3419,plain,
% 1.44/1.64 (~(s(s(z)) = s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3418, 1285])).
% 1.44/1.64 tff(3420,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3421,plain,
% 1.44/1.64 (((~b(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(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~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)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3422,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3421])).
% 1.44/1.64 tff(3423,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3422, 3420])).
% 1.44/1.65 tff(3424,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3425,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 1.44/1.65 tff(3426,plain,
% 1.44/1.65 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3425, 337, 1858, 821, 1274])).
% 1.44/1.65 tff(3427,plain,
% 1.44/1.65 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1133, 3426, 230])).
% 1.44/1.65 tff(3428,plain,
% 1.44/1.65 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[579, 3427, 428])).
% 1.44/1.65 tff(3429,plain,
% 1.44/1.65 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3428, 3175])).
% 1.44/1.65 tff(3430,plain,
% 1.44/1.65 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3429, 3174])).
% 1.44/1.65 tff(3431,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1182])).
% 1.44/1.65 tff(3432,plain,
% 1.44/1.65 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3431])).
% 1.44/1.65 tff(3433,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3434,plain,
% 1.44/1.65 (((~b(s(s(s(s(z)))), z)) | (~b(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3435,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3434])).
% 1.44/1.65 tff(3436,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3435, 3433])).
% 1.44/1.65 tff(3437,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3438,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3437, 3436])).
% 1.44/1.65 tff(3439,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3438, 337, 1858, 821, 1274])).
% 1.44/1.65 tff(3440,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3439, 3432])).
% 1.44/1.65 tff(3441,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[363, 3440, 172])).
% 1.44/1.65 tff(3442,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3441, 3216])).
% 1.44/1.65 tff(3443,plain,
% 1.44/1.65 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1102])).
% 1.44/1.65 tff(3444,plain,
% 1.44/1.65 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[3443])).
% 1.44/1.65 tff(3445,plain,
% 1.44/1.65 ((~r(s(z), s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3444])).
% 1.44/1.65 tff(3446,plain,
% 1.44/1.65 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.65 tff(3447,plain,
% 1.44/1.65 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3446])).
% 1.44/1.65 tff(3448,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[1165])).
% 1.44/1.65 tff(3449,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1164])).
% 1.44/1.65 tff(3450,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(transitivity,[status(thm)],[3449, 3448])).
% 1.44/1.65 tff(3451,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[811, 3450])).
% 1.44/1.65 tff(3452,plain,
% 1.44/1.65 (~r(elem!1, s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2551, 3441, 3451])).
% 1.44/1.65 tff(3453,plain,
% 1.44/1.65 (~r(s(z), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3452, 3447])).
% 1.44/1.65 tff(3454,plain,
% 1.44/1.65 (~r(s(z), s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3453, 3445])).
% 1.44/1.65 tff(3455,plain,
% 1.44/1.65 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.44/1.65 inference(commutativity,[status(thm)],[])).
% 1.44/1.65 tff(3456,plain,
% 1.44/1.65 ((s(z) = s(s(z))) <=> (s(z) = s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1102])).
% 1.44/1.65 tff(3457,plain,
% 1.44/1.65 ((s(z) = s(s(z))) <=> (s(elem!1) = s(z))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3456, 3455])).
% 1.44/1.65 tff(3458,plain,
% 1.44/1.65 ((s(elem!1) = s(z)) <=> (s(z) = s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[3457])).
% 1.44/1.65 tff(3459,plain,
% 1.44/1.65 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3458])).
% 1.44/1.65 tff(3460,plain,
% 1.44/1.65 (~(s(z) = s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[50, 3459])).
% 1.44/1.65 tff(3461,plain,
% 1.44/1.65 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3384, 43])).
% 1.44/1.65 tff(3462,plain,
% 1.44/1.65 (b(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3461, 3460, 3454])).
% 1.44/1.65 tff(3463,plain,
% 1.44/1.65 (b(elem!1, s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1015, 3452, 981])).
% 1.44/1.65 tff(3464,plain,
% 1.44/1.65 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1268, 3108])).
% 1.44/1.65 tff(3465,plain,
% 1.44/1.65 ((~r(s(z), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3464])).
% 1.44/1.65 tff(3466,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.65 tff(3467,plain,
% 1.44/1.65 (r(s(s(s(z))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1498, 1599])).
% 1.44/1.65 tff(3468,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3469,plain,
% 1.44/1.65 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3470,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3469])).
% 1.44/1.65 tff(3471,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3470, 3468])).
% 1.44/1.65 tff(3472,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3473,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3472, 3471])).
% 1.44/1.65 tff(3474,plain,
% 1.44/1.65 (~r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3473, 189, 3134, 3467])).
% 1.44/1.65 tff(3475,plain,
% 1.44/1.65 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2796, 43, 3474])).
% 1.44/1.65 tff(3476,plain,
% 1.44/1.65 (b(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3475, 2781])).
% 1.44/1.65 tff(3477,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(3478,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3479,plain,
% 1.44/1.65 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3480,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3479])).
% 1.44/1.65 tff(3481,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3480, 3478])).
% 1.44/1.65 tff(3482,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3483,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 1.44/1.65 tff(3484,plain,
% 1.44/1.65 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3483, 337, 2, 1592, 3477, 1274])).
% 1.44/1.65 tff(3485,plain,
% 1.44/1.65 (~b(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3484, 3476])).
% 1.44/1.65 tff(3486,plain,
% 1.44/1.65 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1360, 43, 458, 3485])).
% 1.44/1.65 tff(3487,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3226, 189, 1397, 3486])).
% 1.44/1.65 tff(3488,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[524, 3487])).
% 1.44/1.65 tff(3489,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3490,plain,
% 1.44/1.65 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3491,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3490])).
% 1.44/1.65 tff(3492,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3491, 3489])).
% 1.44/1.65 tff(3493,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3494,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 1.44/1.65 tff(3495,plain,
% 1.44/1.65 (~b(s(s(z)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3494, 337, 2, 1591, 3477, 1274, 3476])).
% 1.44/1.65 tff(3496,plain,
% 1.44/1.65 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1298, 43, 3495])).
% 1.44/1.65 tff(3497,plain,
% 1.44/1.65 (r(s(s(z)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3496, 1286])).
% 1.44/1.65 tff(3498,plain,
% 1.44/1.65 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3249, 337, 3243, 2])).
% 1.44/1.65 tff(3499,plain,
% 1.44/1.65 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3498, 3242])).
% 1.44/1.65 tff(3500,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3499, 3241])).
% 1.44/1.65 tff(3501,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3252, 3500])).
% 1.44/1.65 tff(3502,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3501, 3239])).
% 1.44/1.65 tff(3503,plain,
% 1.44/1.65 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[3261])).
% 1.44/1.65 tff(3504,plain,
% 1.44/1.65 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3109])).
% 1.44/1.65 tff(3505,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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))))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3506,plain,
% 1.44/1.65 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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))))), z))) <=> ((~b(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3507,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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))))), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3506])).
% 1.44/1.65 tff(3508,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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))))), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3507, 3505])).
% 1.44/1.65 tff(3509,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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))))), z)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3510,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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))))), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 1.44/1.65 tff(3511,plain,
% 1.44/1.65 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3510, 337, 3243, 2, 1592])).
% 1.44/1.65 tff(3512,plain,
% 1.44/1.65 (~b(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3511, 3242])).
% 1.44/1.65 tff(3513,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3512, 3504])).
% 1.44/1.65 tff(3514,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[663, 3513])).
% 1.44/1.65 tff(3515,plain,
% 1.44/1.65 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3285, 3514, 274])).
% 1.44/1.65 tff(3516,plain,
% 1.44/1.65 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3274, 3515, 3260])).
% 1.44/1.65 tff(3517,plain,
% 1.44/1.65 (b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3516, 3503])).
% 1.44/1.65 tff(3518,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(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(X1, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3519,plain,
% 1.44/1.65 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3520,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(X1, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3519])).
% 1.44/1.65 tff(3521,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(X1, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3520, 3518])).
% 1.44/1.65 tff(3522,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3523,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 1.44/1.66 tff(3524,plain,
% 1.44/1.66 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3523, 337, 1591, 3477, 1274, 3242, 3517])).
% 1.44/1.66 tff(3525,plain,
% 1.44/1.66 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3299, 3524, 3255])).
% 1.44/1.66 tff(3526,plain,
% 1.44/1.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3308, 3525])).
% 1.44/1.66 tff(3527,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3526, 3502])).
% 1.44/1.66 tff(3528,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3529,plain,
% 1.44/1.66 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3528, 3497, 230, 1591, 3477, 1274, 274, 3488, 2, 1592])).
% 1.44/1.66 tff(3530,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3529, 3132])).
% 1.44/1.66 tff(3531,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[700, 3530, 3466])).
% 1.44/1.66 tff(3532,plain,
% 1.44/1.66 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3531, 3114])).
% 1.44/1.66 tff(3533,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3534,plain,
% 1.44/1.66 (((~b(s(s(s(s(z)))), 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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3535,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3534])).
% 1.44/1.66 tff(3536,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3535, 3533])).
% 1.44/1.66 tff(3537,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(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)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3538,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 1.44/1.66 tff(3539,plain,
% 1.44/1.66 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3538, 337, 2, 1591, 3476])).
% 1.44/1.66 tff(3540,plain,
% 1.44/1.66 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3539, 3488])).
% 1.44/1.66 tff(3541,plain,
% 1.44/1.66 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1150, 3540])).
% 1.44/1.66 tff(3542,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3543,plain,
% 1.44/1.66 (((~r(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(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3544,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3543])).
% 1.44/1.66 tff(3545,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3544, 3542])).
% 1.44/1.66 tff(3546,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3547,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.44/1.66 tff(3548,plain,
% 1.44/1.66 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3547, 189, 3541])).
% 1.44/1.66 tff(3549,plain,
% 1.44/1.66 (~r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3548, 3532])).
% 1.44/1.66 tff(3550,plain,
% 1.44/1.66 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3549, 3465])).
% 1.44/1.66 tff(3551,plain,
% 1.44/1.66 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3274, 3550, 3260])).
% 1.44/1.66 tff(3552,plain,
% 1.44/1.66 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.66 tff(3553,plain,
% 1.44/1.66 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[3552])).
% 1.44/1.66 tff(3554,plain,
% 1.44/1.66 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3553])).
% 1.44/1.66 tff(3555,plain,
% 1.44/1.66 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[211, 3554])).
% 1.44/1.66 tff(3556,plain,
% 1.44/1.66 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[632, 3555])).
% 1.44/1.66 tff(3557,plain,
% 1.44/1.66 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3108, 1102])).
% 1.44/1.66 tff(3558,plain,
% 1.44/1.66 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3557])).
% 1.44/1.66 tff(3559,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.66 tff(3560,plain,
% 1.44/1.66 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3559, 3174])).
% 1.44/1.66 tff(3561,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3562,plain,
% 1.44/1.66 (((~r(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(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(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3563,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3562])).
% 1.44/1.66 tff(3564,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.44/1.66 tff(3565,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3566,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.44/1.66 tff(3567,plain,
% 1.44/1.66 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3566, 189])).
% 1.44/1.66 tff(3568,plain,
% 1.44/1.66 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3567, 3560, 3532])).
% 1.44/1.66 tff(3569,plain,
% 1.44/1.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3568, 3558])).
% 1.44/1.66 tff(3570,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[649, 3569, 3556])).
% 1.44/1.66 tff(3571,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.44/1.66 tff(3572,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.66 tff(3573,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(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(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3574,plain,
% 1.44/1.66 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3575,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), 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(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3574])).
% 1.44/1.66 tff(3576,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), 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(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.44/1.66 tff(3577,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), 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)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3578,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.44/1.66 tff(3579,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3578, 337, 3572, 2520, 982, 3571])).
% 1.44/1.66 tff(3580,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3581,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3580, 3570, 3551, 2520, 982])).
% 1.44/1.66 tff(3582,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~(elem!1 = s(z))) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (s(s(s(z))) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3583,plain,
% 1.44/1.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3582, 3463, 2520, 230, 3429, 3130, 821, 3462, 1274, 274, 1858, 3418, 3442])).
% 1.44/1.66 tff(3584,plain,
% 1.44/1.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[548, 3583])).
% 1.44/1.66 tff(3585,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3586,plain,
% 1.44/1.66 (((~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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3587,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3586])).
% 1.44/1.66 tff(3588,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.44/1.66 tff(3589,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3590,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.44/1.66 tff(3591,plain,
% 1.44/1.66 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3590, 189, 3584])).
% 1.44/1.66 tff(3592,plain,
% 1.44/1.66 (~r(s(s(z)), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3591, 3430])).
% 1.44/1.66 tff(3593,plain,
% 1.44/1.66 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1298, 43, 3592])).
% 1.44/1.66 tff(3594,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3593, 3419])).
% 1.44/1.66 tff(3595,plain,
% 1.44/1.66 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1355, 189, 3584])).
% 1.44/1.66 tff(3596,plain,
% 1.44/1.66 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3595, 3430])).
% 1.44/1.66 tff(3597,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1360, 43, 3418, 3596])).
% 1.44/1.66 tff(3598,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3599,plain,
% 1.44/1.66 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3600,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), 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(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3599])).
% 1.44/1.67 tff(3601,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), 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(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3600, 3598])).
% 1.44/1.67 tff(3602,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), 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))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3603,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 1.44/1.67 tff(3604,plain,
% 1.44/1.67 (~b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3603, 337, 3462, 3597, 3594])).
% 1.44/1.67 tff(3605,plain,
% 1.44/1.67 (r(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[48, 3604])).
% 1.44/1.67 tff(3606,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3607,plain,
% 1.44/1.67 (((~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(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3608,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3607])).
% 1.44/1.67 tff(3609,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3608, 3606])).
% 1.44/1.67 tff(3610,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3611,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 1.44/1.67 tff(3612,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3611, 189, 3584, 811, 3605])).
% 1.44/1.67 tff(3613,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3614,plain,
% 1.44/1.67 (~r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3613, 811, 2520, 1274, 230, 50, 172, 173])).
% 1.44/1.67 tff(3615,plain,
% 1.44/1.67 (b(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1759, 3614, 1900])).
% 1.44/1.67 tff(3616,plain,
% 1.44/1.67 (b(s(z), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3615, 3103])).
% 1.44/1.67 tff(3617,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), 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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3618,plain,
% 1.44/1.67 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), 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(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3619,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3618])).
% 1.44/1.67 tff(3620,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3619, 3617])).
% 1.44/1.67 tff(3621,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3622,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3621, 3620])).
% 1.44/1.67 tff(3623,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3622, 337, 3616, 3417, 1591, 1274, 3357])).
% 1.44/1.67 tff(3624,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~r(z, s(z))) | (elem!1 = z) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3625,plain,
% 1.44/1.67 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3624, 3413, 3091, 3414, 3080, 173, 3082, 3079, 3077, 172])).
% 1.44/1.67 tff(3626,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[851, 3625])).
% 1.44/1.67 tff(3627,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3080])).
% 1.44/1.67 tff(3628,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(symmetry,[status(thm)],[3627])).
% 1.44/1.67 tff(3629,plain,
% 1.44/1.67 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3089])).
% 1.44/1.67 tff(3630,plain,
% 1.44/1.67 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3629])).
% 1.44/1.67 tff(3631,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3630])).
% 1.44/1.67 tff(3632,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3631])).
% 1.44/1.67 tff(3633,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(transitivity,[status(thm)],[3632, 3628])).
% 1.44/1.67 tff(3634,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3626, 3633])).
% 1.44/1.67 tff(3635,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3630])).
% 1.44/1.67 tff(3636,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 1.44/1.67 inference(symmetry,[status(thm)],[3635])).
% 1.44/1.67 tff(3637,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3413, 3636])).
% 1.44/1.67 tff(3638,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3626, 3632])).
% 1.44/1.67 tff(3639,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.67 tff(3640,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3641,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), z)) | (~b(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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3642,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3641])).
% 1.44/1.67 tff(3643,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3642, 3640])).
% 1.44/1.67 tff(3644,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(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)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3645,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3644, 3643])).
% 1.44/1.67 tff(3646,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3645, 337, 1763, 326, 1925, 3639])).
% 1.44/1.67 tff(3647,plain,((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3648,plain,
% 1.44/1.67 (~b(z, s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3647, 1763, 3639, 326])).
% 1.44/1.67 tff(3649,plain,
% 1.44/1.67 (r(z, s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[146, 3648])).
% 1.44/1.67 tff(3650,plain,
% 1.44/1.67 (r(z, s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3047, 3649, 230])).
% 1.44/1.67 tff(3651,plain,
% 1.44/1.67 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1580, 3650, 173])).
% 1.44/1.67 tff(3652,plain,
% 1.44/1.67 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1150, 3651])).
% 1.44/1.67 tff(3653,plain,
% 1.44/1.67 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3652, 3219])).
% 1.44/1.67 tff(3654,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2144, 3653, 1544, 241])).
% 1.44/1.67 tff(3655,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[363, 3654, 172])).
% 1.44/1.67 tff(3656,plain,
% 1.44/1.67 (~r(z, s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1082, 3655, 3649])).
% 1.44/1.67 tff(3657,plain,
% 1.44/1.67 (b(z, s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[395, 3656])).
% 1.44/1.67 tff(3658,plain,
% 1.44/1.67 (b(z, s(s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3657, 3100])).
% 1.44/1.67 tff(3659,plain,
% 1.44/1.67 (b(s(z), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1763, 3103])).
% 1.44/1.67 tff(3660,plain,
% 1.44/1.67 (~b(z, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3365, 3659, 1274, 3098])).
% 1.44/1.67 tff(3661,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3660, 3658])).
% 1.44/1.67 tff(3662,plain,((~b(elem!1, z)) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3663,plain,
% 1.44/1.67 (~b(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3662, 3080, 172, 3078, 3638, 3091, 173, 3637, 3634])).
% 1.44/1.67 tff(3664,plain,
% 1.44/1.67 (r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1759, 3663, 3082])).
% 1.44/1.67 tff(3665,plain,
% 1.44/1.67 (r(elem!1, s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1144, 1141, 230])).
% 1.44/1.67 tff(3666,plain,
% 1.44/1.67 (~r(z, s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[291, 3665, 274])).
% 1.44/1.67 tff(3667,plain,
% 1.44/1.67 (b(z, s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[146, 3666])).
% 1.44/1.67 tff(3668,plain,
% 1.44/1.67 (b(z, s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3667, 3400])).
% 1.44/1.67 tff(3669,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z)))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3670,plain,
% 1.44/1.67 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(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(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(z))) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3671,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z)))), s(z))) | (~b(s(s(z)), z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3670])).
% 1.44/1.67 tff(3672,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3671, 3669])).
% 1.44/1.67 tff(3673,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3674,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(z)))), s(z))) | (~b(s(s(z)), z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3673, 3672])).
% 1.44/1.67 tff(3675,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3674, 337, 1231, 3668, 1591, 1274])).
% 1.44/1.67 tff(3676,plain,
% 1.44/1.67 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1133, 3675, 230])).
% 1.44/1.67 tff(3677,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[579, 3676, 983])).
% 1.44/1.67 tff(3678,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3677, 3175])).
% 1.44/1.67 tff(3679,plain,
% 1.44/1.67 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3678, 3174])).
% 1.44/1.67 tff(3680,plain,
% 1.44/1.67 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1356, 3679])).
% 1.44/1.67 tff(3681,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1360, 43, 458, 3680])).
% 1.44/1.67 tff(3682,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3683,plain,
% 1.44/1.67 (((~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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3684,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3683])).
% 1.44/1.67 tff(3685,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3684, 3682])).
% 1.44/1.67 tff(3686,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3687,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.44/1.67 tff(3688,plain,
% 1.44/1.67 (~r(s(z), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3687, 189, 1141, 1339])).
% 1.44/1.67 tff(3689,plain,
% 1.44/1.67 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2796, 43, 3688])).
% 1.44/1.67 tff(3690,plain,
% 1.44/1.67 (b(s(z), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3689, 2781])).
% 1.44/1.67 tff(3691,plain,
% 1.44/1.67 (~r(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1616, 189, 1141, 1339])).
% 1.44/1.67 tff(3692,plain,
% 1.44/1.67 (b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[48, 3691])).
% 1.44/1.67 tff(3693,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3694,plain,
% 1.44/1.67 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3695,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(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(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3694])).
% 1.44/1.67 tff(3696,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(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(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3695, 3693])).
% 1.44/1.67 tff(3697,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3698,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.44/1.67 tff(3699,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3698, 337, 3692, 3094, 3690, 3681])).
% 1.44/1.67 tff(3700,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3701,plain,
% 1.44/1.67 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3700, 1339, 458, 230, 1544, 983, 1231, 1591, 1274, 274])).
% 1.44/1.67 tff(3702,plain,
% 1.44/1.67 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1150, 3701])).
% 1.44/1.67 tff(3703,plain,
% 1.44/1.67 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3056, 337, 3702, 1231])).
% 1.44/1.67 tff(3704,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3703, 3094])).
% 1.44/1.67 tff(3705,plain,
% 1.44/1.67 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1133, 3704, 230])).
% 1.44/1.67 tff(3706,plain,
% 1.44/1.68 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[579, 3705, 983])).
% 1.44/1.68 tff(3707,plain,
% 1.44/1.68 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3706, 3175])).
% 1.44/1.68 tff(3708,plain,
% 1.44/1.68 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3707, 3174])).
% 1.44/1.68 tff(3709,plain,
% 1.44/1.68 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1356, 3708])).
% 1.44/1.68 tff(3710,plain,
% 1.44/1.68 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1360, 43, 458, 3709])).
% 1.44/1.68 tff(3711,plain,
% 1.44/1.68 (~r(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2866, 3710, 1274, 173])).
% 1.44/1.68 tff(3712,plain,
% 1.44/1.68 (b(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[48, 3711])).
% 1.44/1.68 tff(3713,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(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(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3714,plain,
% 1.44/1.68 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3715,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(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(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3714])).
% 1.44/1.68 tff(3716,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(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(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3715, 3713])).
% 1.44/1.68 tff(3717,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3718,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 1.44/1.68 tff(3719,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3718, 337, 3702, 1231, 3712, 3094, 3710])).
% 1.44/1.68 tff(3720,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (s(s(s(z))) = s(s(z))) | (~(elem!1 = s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3721,plain,
% 1.44/1.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3720, 3664, 3091, 173, 3081, 3080, 428, 3078, 3413, 3626])).
% 1.44/1.68 tff(3722,plain,
% 1.44/1.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[548, 3721])).
% 1.44/1.68 tff(3723,plain,
% 1.44/1.68 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1144, 739, 230])).
% 1.44/1.68 tff(3724,plain,
% 1.44/1.68 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1150, 3723])).
% 1.44/1.68 tff(3725,plain,
% 1.44/1.68 (~b(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1281, 337, 3724, 2, 1231])).
% 1.44/1.68 tff(3726,plain,
% 1.44/1.68 (r(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[48, 3725])).
% 1.44/1.68 tff(3727,plain,
% 1.44/1.68 (~r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1766, 189, 173, 3726])).
% 1.44/1.68 tff(3728,plain,
% 1.44/1.68 (b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1498, 3727])).
% 1.44/1.68 tff(3729,plain,
% 1.44/1.68 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[230])).
% 1.44/1.68 tff(3730,plain,
% 1.44/1.68 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3729])).
% 1.44/1.68 tff(3731,plain,
% 1.44/1.68 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3219, 3730])).
% 1.44/1.68 tff(3732,plain,
% 1.44/1.68 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3724, 3731])).
% 1.44/1.68 tff(3733,plain,
% 1.44/1.68 (~r(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2530, 3732, 172, 2520, 981, 274, 215])).
% 1.44/1.68 tff(3734,plain,
% 1.44/1.68 (b(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[395, 3733])).
% 1.44/1.68 tff(3735,plain,
% 1.44/1.68 (b(z, s(s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3734, 3100])).
% 1.44/1.68 tff(3736,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z)), z)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3737,plain,
% 1.44/1.68 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z, 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(z)), z)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3738,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z)), z))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3737])).
% 1.44/1.68 tff(3739,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z)), z)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3738, 3736])).
% 1.44/1.68 tff(3740,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3741,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 1.44/1.68 tff(3742,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3741, 337, 2, 1591, 1274, 3735, 3728])).
% 1.44/1.68 tff(3743,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3744,plain,
% 1.44/1.68 (~r(z, s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3743, 3722, 3413, 3091, 173, 3080, 172, 3079, 3664, 3626])).
% 1.44/1.68 tff(3745,plain,
% 1.44/1.68 (b(z, s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[146, 3744])).
% 1.44/1.68 tff(3746,plain,
% 1.44/1.68 (b(z, s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3403, 3745, 3080])).
% 1.44/1.68 tff(3747,plain,
% 1.44/1.68 (~b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1598, 337, 3722, 3746, 3413])).
% 1.44/1.68 tff(3748,plain,
% 1.44/1.68 (r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1498, 3747])).
% 1.44/1.68 tff(3749,plain,
% 1.44/1.68 (r(elem!1, z) <=> r(s(z), z)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3080])).
% 1.44/1.68 tff(3750,plain,
% 1.44/1.68 (r(s(z), z)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3664, 3749])).
% 1.44/1.68 tff(3751,plain,
% 1.44/1.68 (~r(s(z), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3473, 189, 3750, 3748])).
% 1.44/1.68 tff(3752,plain,
% 1.44/1.68 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2796, 43, 3751])).
% 1.44/1.68 tff(3753,plain,
% 1.44/1.68 (b(s(z), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3752, 2781])).
% 1.44/1.68 tff(3754,plain,
% 1.44/1.68 (~r(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1316, 189, 3750, 3748])).
% 1.44/1.68 tff(3755,plain,
% 1.44/1.68 (b(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[48, 3754])).
% 1.44/1.68 tff(3756,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3757,plain,
% 1.44/1.68 (((~b(s(s(s(z))), s(z))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3758,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3757])).
% 1.44/1.68 tff(3759,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3758, 3756])).
% 1.44/1.68 tff(3760,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3761,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 1.44/1.68 tff(3762,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3761, 337, 3722, 3626, 3755, 3753])).
% 1.44/1.68 tff(3763,plain,(r(elem!1, s(z)) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1) | (~b(s(elem!1), z)) | r(s(z), elem!1) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3764,plain,
% 1.44/1.68 (r(s(elem!1), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3763, 3061, 81, 172, 3038, 3035, 3037])).
% 1.44/1.68 tff(3765,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3764, 3036])).
% 1.44/1.68 tff(3766,plain,((~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (z = elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3767,plain,
% 1.44/1.68 (~(elem!1 = s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3766, 172, 147, 118, 2969, 3028, 61, 69])).
% 1.44/1.68 tff(3768,plain,
% 1.44/1.68 (~(elem!1 = z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[67, 65])).
% 1.44/1.68 tff(3769,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2031, 1762, 1761, 118, 173, 1603, 247])).
% 1.44/1.68 tff(3770,plain,((~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3771,plain,
% 1.44/1.68 (~r(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3770, 247, 173, 1603, 118])).
% 1.44/1.68 tff(3772,plain,
% 1.44/1.68 (b(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[921, 3771, 65])).
% 1.44/1.68 tff(3773,plain,
% 1.44/1.68 (~b(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2717, 3772, 2520, 600])).
% 1.44/1.68 tff(3774,plain,
% 1.44/1.68 (r(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1759, 3773, 3768])).
% 1.44/1.68 tff(3775,plain,
% 1.44/1.68 (~r(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1709, 3774, 173])).
% 1.44/1.68 tff(3776,plain,
% 1.44/1.68 (~b(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2563, 3774, 172, 2520, 3772, 82])).
% 1.44/1.68 tff(3777,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[322, 3776, 3775, 247])).
% 1.44/1.68 tff(3778,plain,((elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(z, s(elem!1))) | (z = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3779,plain,
% 1.44/1.68 (~b(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3778, 3767, 3028, 82, 81, 172, 61, 2969, 118])).
% 1.44/1.68 tff(3780,plain,
% 1.44/1.68 (r(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[395, 3779])).
% 1.44/1.68 tff(3781,plain,
% 1.44/1.68 (~b(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2707, 3780, 81, 172, 147, 3028, 50])).
% 1.44/1.68 tff(3782,plain,
% 1.44/1.68 (r(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1759, 3781, 68])).
% 1.44/1.68 tff(3783,plain,
% 1.44/1.68 (~r(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1709, 3782, 81])).
% 1.44/1.68 tff(3784,plain,
% 1.44/1.68 (~r(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3770, 3767, 81, 2969, 118])).
% 1.44/1.68 tff(3785,plain,
% 1.44/1.68 (b(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[921, 3784, 61])).
% 1.44/1.68 tff(3786,plain,
% 1.44/1.68 (~b(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2563, 3782, 172, 3028, 3785, 82])).
% 1.44/1.68 tff(3787,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[322, 3786, 3783, 3767])).
% 1.44/1.68 tff(3788,plain,((s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3789,plain,
% 1.44/1.68 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3788, 69, 50, 118, 82])).
% 1.44/1.68 tff(3790,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3789])).
% 1.44/1.68 tff(3791,plain,
% 1.44/1.68 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3790])).
% 1.44/1.68 tff(3792,plain,
% 1.44/1.68 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3789])).
% 1.44/1.68 tff(3793,plain,
% 1.44/1.68 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3792])).
% 1.44/1.68 tff(3794,plain,
% 1.44/1.68 (elem!1 = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[92, 3793, 87, 3791])).
% 1.44/1.68 tff(3795,plain,
% 1.44/1.68 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3794])).
% 1.44/1.68 tff(3796,plain,
% 1.44/1.68 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.68 inference(symmetry,[status(thm)],[3795])).
% 1.44/1.68 tff(3797,plain,
% 1.44/1.68 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3796])).
% 1.44/1.68 tff(3798,plain,
% 1.44/1.68 (~(s(s(s(z))) = elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[116, 3797])).
% 1.44/1.68 tff(3799,plain,
% 1.44/1.68 (~r(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[195, 189, 81, 118])).
% 1.44/1.68 tff(3800,plain,
% 1.44/1.68 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[199, 43, 3799])).
% 1.44/1.68 tff(3801,plain,
% 1.44/1.68 (b(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3800, 179])).
% 1.44/1.68 tff(3802,plain,
% 1.44/1.68 (~r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1768, 81, 118])).
% 1.44/1.68 tff(3803,plain,
% 1.44/1.68 (b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1498, 3802])).
% 1.44/1.68 tff(3804,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = elem!1),
% 1.44/1.68 inference(transitivity,[status(thm)],[3790, 121, 3792, 91])).
% 1.44/1.68 tff(3805,plain,
% 1.44/1.68 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3804])).
% 1.44/1.68 tff(3806,plain,
% 1.44/1.68 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3805])).
% 1.44/1.68 tff(3807,plain,
% 1.44/1.68 (~(elem!1 = s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[135, 3806])).
% 1.44/1.68 tff(3808,plain,
% 1.44/1.68 (~r(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3770, 3807, 81, 2969, 118])).
% 1.44/1.68 tff(3809,plain,
% 1.44/1.68 (b(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[921, 3808, 61])).
% 1.44/1.68 tff(3810,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3789])).
% 1.44/1.68 tff(3811,plain,
% 1.44/1.68 (b(s(elem!1), s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2971, 3810])).
% 1.44/1.68 tff(3812,plain,
% 1.44/1.68 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2743, 3807, 3789])).
% 1.44/1.68 tff(3813,plain,
% 1.44/1.68 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3789])).
% 1.44/1.68 tff(3814,plain,
% 1.44/1.68 (r(z, s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[147, 3813])).
% 1.44/1.68 tff(3815,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2980, 337, 925, 1763, 1603])).
% 1.44/1.68 tff(3816,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1792, 3815])).
% 1.44/1.68 tff(3817,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2023, 3816, 173])).
% 1.44/1.68 tff(3818,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[851, 3817])).
% 1.44/1.68 tff(3819,plain,
% 1.44/1.68 (~b(z, s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2992, 1763, 1603, 925])).
% 1.44/1.68 tff(3820,plain,
% 1.44/1.68 (r(z, s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1786, 3819])).
% 1.44/1.68 tff(3821,plain,
% 1.44/1.68 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1580, 3820, 173])).
% 1.44/1.68 tff(3822,plain,
% 1.44/1.68 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1150, 3821])).
% 1.44/1.68 tff(3823,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2107, 337, 1544, 3822, 3818])).
% 1.44/1.68 tff(3824,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[832, 43, 829, 3823])).
% 1.44/1.68 tff(3825,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2966, 189, 1077, 3816, 3824])).
% 1.44/1.68 tff(3826,plain,((~b(elem!1, z)) | (~r(z, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3827,plain,
% 1.44/1.68 (~b(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3826, 3814, 3812, 3811, 81, 3809, 2969])).
% 1.44/1.68 tff(3828,plain,
% 1.44/1.68 (r(elem!1, z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1759, 3827, 68])).
% 1.44/1.68 tff(3829,plain,
% 1.44/1.68 (~r(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1709, 3828, 81])).
% 1.44/1.68 tff(3830,plain,
% 1.44/1.68 (r(s(z), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2031, 3829, 118, 81, 2969, 3807])).
% 1.44/1.68 tff(3831,plain,
% 1.44/1.68 (~r(s(z), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2896, 3830, 3828])).
% 1.44/1.68 tff(3832,plain,
% 1.44/1.68 (b(s(z), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[963, 3831])).
% 1.44/1.68 tff(3833,plain,
% 1.44/1.68 (b(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[322, 3829, 3807])).
% 1.44/1.68 tff(3834,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3835,plain,
% 1.44/1.68 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3836,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3835])).
% 1.44/1.68 tff(3837,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3836, 3834])).
% 1.44/1.68 tff(3838,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3839,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 1.44/1.69 tff(3840,plain,
% 1.44/1.69 (~b(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3839, 337, 3809, 3833, 3832, 3803, 3801])).
% 1.44/1.69 tff(3841,plain,
% 1.44/1.69 (r(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2463, 3840, 3798])).
% 1.44/1.69 tff(3842,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2057, 189, 3830, 118, 3841])).
% 1.44/1.69 tff(3843,plain,(b(z, s(z)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3844,plain,
% 1.44/1.69 (b(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3843, 82, 50, 118])).
% 1.44/1.69 tff(3845,plain,
% 1.44/1.69 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[93])).
% 1.44/1.69 tff(3846,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3845])).
% 1.44/1.69 tff(3847,plain,
% 1.44/1.69 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[93])).
% 1.44/1.69 tff(3848,plain,
% 1.44/1.69 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3847])).
% 1.44/1.69 tff(3849,plain,
% 1.44/1.69 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[123])).
% 1.44/1.69 tff(3850,plain,
% 1.44/1.69 (~(elem!1 = s(z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[135, 3849])).
% 1.44/1.69 tff(3851,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3852,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3853,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3852, 3851])).
% 1.44/1.69 tff(3854,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3853, 189, 370, 1735, 275])).
% 1.44/1.69 tff(3855,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3856,plain,
% 1.44/1.69 (~r(s(z), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3855, 370, 275])).
% 1.44/1.69 tff(3857,plain,
% 1.44/1.69 (b(s(z), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[727, 3856, 136])).
% 1.44/1.69 tff(3858,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[317, 189, 274, 777, 275])).
% 1.44/1.69 tff(3859,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3860,plain,
% 1.44/1.69 (~r(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3859, 274, 275])).
% 1.44/1.69 tff(3861,plain,
% 1.44/1.69 (b(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[322, 3860, 247])).
% 1.44/1.69 tff(3862,plain,
% 1.44/1.69 (~r(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1493, 3861, 791, 275, 274, 1481])).
% 1.44/1.69 tff(3863,plain,
% 1.44/1.69 (b(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1498, 3862])).
% 1.44/1.69 tff(3864,plain,
% 1.44/1.69 (b(s(s(s(s(z)))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1792, 1542])).
% 1.44/1.69 tff(3865,plain,
% 1.44/1.69 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1795, 2777, 1659, 3864])).
% 1.44/1.69 tff(3866,plain,
% 1.44/1.69 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[548, 3865])).
% 1.44/1.69 tff(3867,plain,
% 1.44/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2027, 3866, 118])).
% 1.44/1.69 tff(3868,plain,
% 1.44/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1150, 3867])).
% 1.44/1.69 tff(3869,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, 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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3870,plain,
% 1.44/1.69 (((~b(z, s(s(s(s(z)))))) | (~b(s(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(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3871,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3870])).
% 1.44/1.69 tff(3872,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3871, 3869])).
% 1.44/1.69 tff(3873,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(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))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3874,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 1.44/1.69 tff(3875,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3874, 337, 1301, 3868, 2777, 3864])).
% 1.44/1.69 tff(3876,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3877,plain,
% 1.44/1.69 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3876, 3863, 118, 1301, 370, 274])).
% 1.44/1.69 tff(3878,plain,
% 1.44/1.69 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[857, 3877, 853])).
% 1.44/1.69 tff(3879,plain,
% 1.44/1.69 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1570, 337, 3861, 791, 3878])).
% 1.44/1.69 tff(3880,plain,
% 1.44/1.69 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1150, 3879])).
% 1.44/1.69 tff(3881,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2027, 3880, 118])).
% 1.44/1.69 tff(3882,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[548, 3881])).
% 1.44/1.69 tff(3883,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3884,plain,
% 1.44/1.69 (((~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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3885,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3884])).
% 1.44/1.69 tff(3886,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3885, 3883])).
% 1.44/1.69 tff(3887,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3888,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(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)))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3887, 3886])).
% 1.44/1.69 tff(3889,plain,
% 1.44/1.69 (~b(z, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3888, 337, 3861, 1301, 3882, 3878, 3863])).
% 1.44/1.69 tff(3890,plain,
% 1.44/1.69 (r(z, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1786, 3889])).
% 1.44/1.69 tff(3891,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3892,plain,
% 1.44/1.69 (((~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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3893,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3892])).
% 1.44/1.69 tff(3894,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3893, 3891])).
% 1.44/1.69 tff(3895,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3896,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 1.44/1.69 tff(3897,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3896, 189, 275, 3880, 3890])).
% 1.44/1.69 tff(3898,plain,((~r(elem!1, z)) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3899,plain,
% 1.44/1.69 (~r(elem!1, z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3898, 3857, 1301, 118, 275, 853, 370, 117, 3850])).
% 1.44/1.69 tff(3900,plain,
% 1.44/1.69 (b(elem!1, z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1759, 3899, 1900])).
% 1.44/1.69 tff(3901,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3902,plain,
% 1.44/1.69 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3903,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3902])).
% 1.44/1.69 tff(3904,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3903, 3901])).
% 1.44/1.69 tff(3905,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3906,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 1.44/1.69 tff(3907,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3906, 337, 1763, 327, 791, 1301])).
% 1.44/1.69 tff(3908,plain,((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3909,plain,
% 1.44/1.69 (~b(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3908, 3900, 1301, 3857])).
% 1.44/1.69 tff(3910,plain,
% 1.44/1.69 (r(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[322, 3909, 3850])).
% 1.44/1.69 tff(3911,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3912,plain,
% 1.44/1.69 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3913,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3912])).
% 1.44/1.69 tff(3914,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3913, 3911])).
% 1.44/1.69 tff(3915,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3916,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3915, 3914])).
% 1.44/1.69 tff(3917,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3916, 189, 3910, 118])).
% 1.44/1.69 tff(3918,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3917, 3848])).
% 1.44/1.69 tff(3919,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3252, 3918])).
% 1.44/1.69 tff(3920,plain,
% 1.44/1.69 (b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3919, 3846])).
% 1.44/1.69 tff(3921,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3922,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3923,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.44/1.69 tff(3924,plain,
% 1.44/1.69 (~r(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3923, 189, 3910, 118])).
% 1.44/1.69 tff(3925,plain,
% 1.44/1.69 (b(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2463, 3924, 117])).
% 1.44/1.69 tff(3926,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1316, 189, 275, 1474, 118])).
% 1.44/1.69 tff(3927,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3928,plain,
% 1.44/1.69 (~r(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3927, 275, 118])).
% 1.44/1.69 tff(3929,plain,
% 1.44/1.69 (b(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1498, 3928])).
% 1.44/1.69 tff(3930,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3931,plain,
% 1.44/1.69 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3932,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3931])).
% 1.44/1.69 tff(3933,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3932, 3930])).
% 1.44/1.69 tff(3934,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3935,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3934, 3933])).
% 1.44/1.69 tff(3936,plain,
% 1.44/1.69 (~b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3935, 337, 3900, 3857, 1301, 3929, 3925])).
% 1.44/1.69 tff(3937,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3936, 3920])).
% 1.44/1.69 tff(3938,plain,((~r(z, elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (elem!1 = z) | (~r(s(z), z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3939,plain,
% 1.44/1.69 (~r(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3938, 275, 3844, 118, 68, 83, 171])).
% 1.44/1.69 tff(3940,plain,
% 1.44/1.69 (b(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[921, 3939, 61])).
% 1.44/1.69 tff(3941,plain,
% 1.44/1.69 (~(s(elem!1) = elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2886, 3939, 148])).
% 1.44/1.69 tff(3942,plain,
% 1.44/1.69 (~(elem!1 = s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[980, 3941])).
% 1.44/1.69 tff(3943,plain,
% 1.44/1.69 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[928, 3940, 82])).
% 1.44/1.69 tff(3944,plain,
% 1.44/1.69 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[281, 3943])).
% 1.44/1.69 tff(3945,plain,
% 1.44/1.69 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[632, 3944])).
% 1.44/1.69 tff(3946,plain,
% 1.44/1.69 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[306, 275, 147])).
% 1.44/1.69 tff(3947,plain,
% 1.44/1.69 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1970, 3946])).
% 1.44/1.69 tff(3948,plain,
% 1.44/1.69 (b(s(elem!1), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[270, 3062, 978])).
% 1.44/1.69 tff(3949,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.44/1.69 tff(3950,plain,
% 1.44/1.69 (~b(s(elem!1), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2913, 83, 984])).
% 1.44/1.69 tff(3951,plain,
% 1.44/1.69 (s(elem!1) = elem!1),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[270, 3950, 3062])).
% 1.44/1.70 tff(3952,plain,
% 1.44/1.70 (elem!1 = s(elem!1)),
% 1.44/1.70 inference(symmetry,[status(thm)],[3951])).
% 1.44/1.70 tff(3953,plain,
% 1.44/1.70 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.44/1.70 inference(transitivity,[status(thm)],[84, 121, 88, 91, 3952])).
% 1.44/1.70 tff(3954,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3949, 3953])).
% 1.44/1.70 tff(3955,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | r(s(elem!1), elem!1) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.70 tff(3956,plain,
% 1.44/1.70 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3955, 3062, 83, 3949])).
% 1.44/1.70 tff(3957,plain,
% 1.44/1.70 (~r(s(z), elem!1)),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2896, 274, 275])).
% 1.44/1.70 tff(3958,plain,
% 1.44/1.70 (b(s(z), elem!1)),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[727, 3957, 2754])).
% 1.44/1.70 tff(3959,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[1979, 3958, 3861, 324, 326])).
% 1.44/1.70 tff(3960,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3961,plain,
% 1.54/1.70 (~r(elem!1, z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3960, 3956, 324, 136, 3850, 275])).
% 1.54/1.70 tff(3962,plain,
% 1.54/1.70 (b(elem!1, z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1759, 3961, 68])).
% 1.54/1.70 tff(3963,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3964,plain,
% 1.54/1.70 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3965,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3964])).
% 1.54/1.70 tff(3966,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3965, 3963])).
% 1.54/1.70 tff(3967,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3968,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3967, 3966])).
% 1.54/1.70 tff(3969,plain,
% 1.54/1.70 (~b(s(elem!1), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3968, 337, 925, 3962, 3948])).
% 1.54/1.70 tff(3970,plain,
% 1.54/1.70 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2743, 3850, 83])).
% 1.54/1.70 tff(3971,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3972,plain,
% 1.54/1.70 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3973,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3972])).
% 1.54/1.70 tff(3974,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3973, 3971])).
% 1.54/1.70 tff(3975,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3976,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 1.54/1.70 tff(3977,plain,
% 1.54/1.70 ((~b(s(elem!1), z)) | (~b(z, elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3976, 337, 1763, 2520, 1301])).
% 1.54/1.70 tff(3978,plain,
% 1.54/1.70 (~b(s(elem!1), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3977, 925])).
% 1.54/1.70 tff(3979,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3980,plain,
% 1.54/1.70 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3981,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3980])).
% 1.54/1.70 tff(3982,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3981, 3979])).
% 1.54/1.70 tff(3983,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3984,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 1.54/1.70 tff(3985,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3984, 337, 925, 1763, 2520, 1603])).
% 1.54/1.70 tff(3986,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[832, 43, 829, 3985])).
% 1.54/1.70 tff(3987,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[820, 43, 817, 3815])).
% 1.54/1.70 tff(3988,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3989,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3990,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 1.54/1.70 tff(3991,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3990, 189, 1219, 3987, 3986])).
% 1.54/1.70 tff(3992,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3993,plain,
% 1.54/1.70 (~r(s(elem!1), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3992, 925, 1603, 2520, 829, 1763])).
% 1.54/1.70 tff(3994,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[378, 43, 114, 3993, 3978])).
% 1.54/1.70 tff(3995,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3996,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3995, 3962, 3970, 1301, 3948, 925])).
% 1.54/1.70 tff(3997,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[857, 3996, 171])).
% 1.54/1.70 tff(3998,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3999,plain,
% 1.54/1.70 (((~b(z, elem!1)) | (~b(s(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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4000,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, 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))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3999])).
% 1.54/1.70 tff(4001,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, 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)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[4000, 3998])).
% 1.54/1.70 tff(4002,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(4003,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[4002, 4001])).
% 1.54/1.70 tff(4004,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4003, 337, 925, 1763, 791, 1301])).
% 1.54/1.70 tff(4005,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(4006,plain,
% 1.54/1.70 (~b(s(z), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4005, 3962, 1301, 925])).
% 1.54/1.70 tff(4007,plain,
% 1.54/1.70 (r(s(z), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[727, 4006, 136])).
% 1.54/1.70 tff(4008,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2079, 189, 4007, 3997])).
% 1.54/1.70 tff(4009,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[851, 4008])).
% 1.54/1.70 tff(4010,plain,
% 1.54/1.70 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[3455])).
% 1.54/1.70 tff(4011,plain,
% 1.54/1.70 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[4010])).
% 1.54/1.70 tff(4012,plain,
% 1.54/1.70 (~(s(z) = s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[50, 4011])).
% 1.54/1.70 tff(4013,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4014,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(4015,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 1.54/1.70 tff(4016,plain,
% 1.54/1.70 (~r(s(z), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4015, 189, 1219, 275])).
% 1.54/1.70 tff(4017,plain,
% 1.54/1.70 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2133, 43, 4016])).
% 1.54/1.70 tff(4018,plain,
% 1.54/1.70 (b(s(z), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4017, 4012])).
% 1.54/1.70 tff(4019,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4020,plain,
% 1.54/1.70 (((~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))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4021,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[4020])).
% 1.54/1.70 tff(4022,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[4021, 4019])).
% 1.54/1.70 tff(4023,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(4024,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 1.54/1.70 tff(4025,plain,
% 1.54/1.70 (~r(s(elem!1), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4024, 189, 1219, 275])).
% 1.54/1.70 tff(4026,plain,
% 1.54/1.70 (b(s(elem!1), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[898, 4025, 50])).
% 1.54/1.70 tff(4027,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4028,plain,
% 1.54/1.70 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(4029,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[4028])).
% 1.54/1.70 tff(4030,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4029, 4027])).
% 1.54/1.71 tff(4031,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4032,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4031, 4030])).
% 1.54/1.71 tff(4033,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4032, 337, 2520, 4026, 1231, 4018])).
% 1.54/1.71 tff(4034,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[832, 43, 829, 4033])).
% 1.54/1.71 tff(4035,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4036,plain,
% 1.54/1.71 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4037,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4036])).
% 1.54/1.71 tff(4038,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4037, 4035])).
% 1.54/1.71 tff(4039,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4040,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 1.54/1.71 tff(4041,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4040, 337, 925, 2520, 1301, 1231, 4018])).
% 1.54/1.71 tff(4042,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[820, 43, 817, 4041])).
% 1.54/1.71 tff(4043,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3990, 189, 1219, 4042, 4034])).
% 1.54/1.71 tff(4044,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4045,plain,
% 1.54/1.71 (~r(s(elem!1), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4044, 4009, 3948, 275, 3970, 925, 1301, 50])).
% 1.54/1.71 tff(4046,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[378, 43, 114, 4045, 3969])).
% 1.54/1.71 tff(4047,plain,(r(s(elem!1), elem!1) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4048,plain,
% 1.54/1.71 (r(s(elem!1), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4047, 275, 3940, 3844, 50, 3947, 83, 3945, 3941])).
% 1.54/1.71 tff(4049,plain,
% 1.54/1.71 (~r(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2578, 1077, 50, 791, 327, 1008, 274])).
% 1.54/1.71 tff(4050,plain,
% 1.54/1.71 (b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[80, 4049])).
% 1.54/1.71 tff(4051,plain,
% 1.54/1.71 (((~b(elem!1, s(z))) | (~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(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4052,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4051])).
% 1.54/1.71 tff(4053,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4052, 1055])).
% 1.54/1.71 tff(4054,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4055,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 1.54/1.71 tff(4056,plain,
% 1.54/1.71 (~b(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4055, 337, 327, 791, 4050])).
% 1.54/1.71 tff(4057,plain,
% 1.54/1.71 (r(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[921, 4056, 61])).
% 1.54/1.71 tff(4058,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[385, 189, 4057, 1077, 273])).
% 1.54/1.71 tff(4059,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4060,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4059, 3958, 3861, 273, 274, 50, 1008, 1077])).
% 1.54/1.71 tff(4061,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(z, s(elem!1))) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4062,plain,
% 1.54/1.71 (~r(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4061, 4048, 50, 3942, 148, 136, 3850, 275])).
% 1.54/1.71 tff(4063,plain,
% 1.54/1.71 (b(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1759, 4062, 68])).
% 1.54/1.71 tff(4064,plain,
% 1.54/1.71 (~b(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2456, 4063, 3929, 3940])).
% 1.54/1.71 tff(4065,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2463, 4064, 117])).
% 1.54/1.71 tff(4066,plain,
% 1.54/1.71 (~b(s(z), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4005, 4063, 3844, 3940])).
% 1.54/1.71 tff(4067,plain,
% 1.54/1.71 (r(s(z), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[727, 4066, 136])).
% 1.54/1.71 tff(4068,plain,
% 1.54/1.71 (~r(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2099, 273, 1735])).
% 1.54/1.71 tff(4069,plain,
% 1.54/1.71 (b(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[898, 4068, 50])).
% 1.54/1.71 tff(4070,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4071,plain,
% 1.54/1.71 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4072,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4071])).
% 1.54/1.71 tff(4073,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4072, 4070])).
% 1.54/1.71 tff(4074,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4075,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4074, 4073])).
% 1.54/1.71 tff(4076,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4075, 337, 925, 327, 4069, 1301, 2134])).
% 1.54/1.71 tff(4077,plain,((~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4078,plain,
% 1.54/1.71 (~b(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4077, 4067, 4048, 3844, 3940, 50])).
% 1.54/1.71 tff(4079,plain,
% 1.54/1.71 (r(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[322, 4078, 3850])).
% 1.54/1.71 tff(4080,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3923, 189, 4079, 118, 4065])).
% 1.54/1.71 tff(4081,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = s(elem!1))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4082,plain,
% 1.54/1.71 (~r(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4081, 83, 50, 118, 82])).
% 1.54/1.71 tff(4083,plain,
% 1.54/1.71 (b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[963, 4082])).
% 1.54/1.71 tff(4084,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3847])).
% 1.54/1.71 tff(4085,plain,
% 1.54/1.71 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3845])).
% 1.54/1.71 tff(4086,plain,
% 1.54/1.71 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[122])).
% 1.54/1.71 tff(4087,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[122])).
% 1.54/1.71 tff(4088,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[4087])).
% 1.54/1.71 tff(4089,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4088, 682])).
% 1.54/1.71 tff(4090,plain,
% 1.54/1.71 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4089])).
% 1.54/1.71 tff(4091,plain,
% 1.54/1.71 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[853, 4090])).
% 1.54/1.71 tff(4092,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4093,plain,
% 1.54/1.71 (((~b(z, s(z))) | (~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(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4094,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4093])).
% 1.54/1.71 tff(4095,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4094, 4092])).
% 1.54/1.71 tff(4096,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4097,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 1.54/1.71 tff(4098,plain,
% 1.54/1.71 (~b(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4097, 337, 327, 1, 1301])).
% 1.54/1.71 tff(4099,plain,
% 1.54/1.71 (r(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1759, 4098, 3768])).
% 1.54/1.71 tff(4100,plain,
% 1.54/1.71 (~b(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[970, 337, 327, 1, 1301])).
% 1.54/1.71 tff(4101,plain,
% 1.54/1.71 (r(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[921, 4100, 65])).
% 1.54/1.71 tff(4102,plain,
% 1.54/1.71 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2760, 853])).
% 1.54/1.71 tff(4103,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.54/1.71 tff(4104,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[870, 189, 370, 1169])).
% 1.54/1.71 tff(4105,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[820, 43, 817, 4104])).
% 1.54/1.71 tff(4106,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2079, 189, 1735, 1169])).
% 1.54/1.71 tff(4107,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[851, 4106])).
% 1.54/1.71 tff(4108,plain,
% 1.54/1.71 (~r(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1743, 370, 1735])).
% 1.54/1.71 tff(4109,plain,
% 1.54/1.71 (b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[80, 4108])).
% 1.54/1.71 tff(4110,plain,
% 1.54/1.71 (~r(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3855, 370, 1735])).
% 1.54/1.71 tff(4111,plain,
% 1.54/1.71 (b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[963, 4110])).
% 1.54/1.71 tff(4112,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4113,plain,
% 1.54/1.71 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4114,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(s(s(z)))), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4113])).
% 1.54/1.71 tff(4115,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(s(s(z)))), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4114, 4112])).
% 1.54/1.71 tff(4116,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4117,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 1.54/1.71 tff(4118,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4117, 337, 4111, 4109, 4107, 4105])).
% 1.54/1.71 tff(4119,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4120,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4119, 1735, 370])).
% 1.54/1.71 tff(4121,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[857, 4120, 853])).
% 1.54/1.71 tff(4122,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2057, 189, 1735, 118, 2465])).
% 1.54/1.71 tff(4123,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4124,plain,
% 1.54/1.71 (~r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4123, 1735, 118])).
% 1.54/1.71 tff(4125,plain,
% 1.54/1.71 (b(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2463, 4124, 117])).
% 1.54/1.71 tff(4126,plain,
% 1.54/1.71 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2027, 1141, 118])).
% 1.54/1.71 tff(4127,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[548, 4126])).
% 1.54/1.71 tff(4128,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4129,plain,
% 1.54/1.71 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4130,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4129])).
% 1.54/1.71 tff(4131,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4130, 4128])).
% 1.54/1.71 tff(4132,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4133,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 1.54/1.72 tff(4134,plain,
% 1.54/1.72 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4133, 337, 327, 4127, 1603, 2454])).
% 1.54/1.72 tff(4135,plain,
% 1.54/1.72 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2845, 43, 2842, 4134])).
% 1.54/1.72 tff(4136,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4137,plain,
% 1.54/1.72 (((~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(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4138,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4137])).
% 1.54/1.72 tff(4139,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4138, 4136])).
% 1.54/1.72 tff(4140,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4141,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4140, 4139])).
% 1.54/1.72 tff(4142,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4141, 189, 1735, 1141, 4135])).
% 1.54/1.72 tff(4143,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4144,plain,
% 1.54/1.72 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4143, 4125, 327, 1735, 4121, 4102, 118])).
% 1.54/1.72 tff(4145,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1150, 4144])).
% 1.54/1.72 tff(4146,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4147,plain,
% 1.54/1.72 (((~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)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4148,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4147])).
% 1.54/1.72 tff(4149,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4148, 4146])).
% 1.54/1.72 tff(4150,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))) | (~b(s(z), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4151,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4150, 4149])).
% 1.54/1.72 tff(4152,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4151, 337, 327, 1, 1301, 1275, 1603, 1592])).
% 1.54/1.72 tff(4153,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4154,plain,
% 1.54/1.72 (~b(z, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4153, 4145, 1301, 327, 4121, 1])).
% 1.54/1.72 tff(4155,plain,
% 1.54/1.72 (r(z, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1786, 4154])).
% 1.54/1.72 tff(4156,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.72 tff(4157,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4158,plain,
% 1.54/1.72 (((~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)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4159,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4158])).
% 1.54/1.72 tff(4160,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4159, 4157])).
% 1.54/1.72 tff(4161,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4162,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.54/1.72 tff(4163,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4162, 189, 274, 1115, 4156])).
% 1.54/1.72 tff(4164,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4165,plain,
% 1.54/1.72 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4164, 4155, 274])).
% 1.54/1.72 tff(4166,plain,
% 1.54/1.72 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[93])).
% 1.54/1.72 tff(4167,plain,
% 1.54/1.72 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[4166])).
% 1.54/1.72 tff(4168,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.72 tff(4169,plain,
% 1.54/1.72 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4168, 4167])).
% 1.54/1.72 tff(4170,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.72 tff(4171,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4170, 4169])).
% 1.54/1.72 tff(4172,plain,(r(elem!1, s(s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4173,plain,
% 1.54/1.72 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4172, 4165, 83])).
% 1.54/1.72 tff(4174,plain,
% 1.54/1.72 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[700, 4173, 4091])).
% 1.54/1.72 tff(4175,plain,
% 1.54/1.72 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4174, 4086])).
% 1.54/1.72 tff(4176,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4177,plain,
% 1.54/1.72 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), 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(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4178,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), 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(X1, 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(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4177])).
% 1.54/1.72 tff(4179,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), 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(X1, 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(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4178, 4176])).
% 1.54/1.72 tff(4180,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), 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))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4181,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4180, 4179])).
% 1.54/1.72 tff(4182,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4181, 337, 327, 4145, 4121, 4175])).
% 1.54/1.72 tff(4183,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4184,plain,
% 1.54/1.72 (~r(s(z), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4183, 327, 83, 4099, 1301, 1, 118, 853, 4101])).
% 1.54/1.72 tff(4185,plain,
% 1.54/1.72 (b(s(z), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[727, 4184, 136])).
% 1.54/1.72 tff(4186,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4187,plain,
% 1.54/1.72 (((~b(s(z), z)) | (~b(s(s(s(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(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4188,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4187])).
% 1.54/1.72 tff(4189,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4188, 4186])).
% 1.54/1.72 tff(4190,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4191,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 1.54/1.72 tff(4192,plain,
% 1.54/1.72 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4191, 337, 1, 1301, 3864])).
% 1.54/1.72 tff(4193,plain,
% 1.54/1.72 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1150, 4192])).
% 1.54/1.72 tff(4194,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2027, 4193, 118])).
% 1.54/1.72 tff(4195,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[548, 4194])).
% 1.54/1.72 tff(4196,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), 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(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4197,plain,
% 1.54/1.72 (((~b(z, s(s(s(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(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(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)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4198,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4197])).
% 1.54/1.72 tff(4199,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4198, 4196])).
% 1.54/1.72 tff(4200,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4201,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4200, 4199])).
% 1.54/1.72 tff(4202,plain,
% 1.54/1.72 (~b(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4201, 337, 4195, 2777, 3864])).
% 1.54/1.72 tff(4203,plain,
% 1.54/1.72 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[199, 43, 4202])).
% 1.54/1.72 tff(4204,plain,
% 1.54/1.72 (r(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4203, 179])).
% 1.54/1.72 tff(4205,plain,
% 1.54/1.72 (~b(s(s(s(z))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3876, 1169, 118, 1301, 370, 274])).
% 1.54/1.72 tff(4206,plain,
% 1.54/1.72 (r(s(s(s(z))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1498, 4205])).
% 1.54/1.72 tff(4207,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4208,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4209,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 1.54/1.73 tff(4210,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4209, 189, 370, 1474, 2465])).
% 1.54/1.73 tff(4211,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4212,plain,
% 1.54/1.73 (~r(s(s(s(z))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4211, 4206, 370])).
% 1.54/1.73 tff(4213,plain,
% 1.54/1.73 (b(s(s(s(z))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2463, 4212, 1481])).
% 1.54/1.73 tff(4214,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4215,plain,
% 1.54/1.73 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4216,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4215])).
% 1.54/1.73 tff(4217,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4216, 4214])).
% 1.54/1.73 tff(4218,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4219,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4218, 4217])).
% 1.54/1.73 tff(4220,plain,
% 1.54/1.73 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4219, 337, 327, 1301, 4195, 3864, 4213])).
% 1.54/1.73 tff(4221,plain,
% 1.54/1.73 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2845, 43, 2842, 4220])).
% 1.54/1.73 tff(4222,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.73 tff(4223,plain,
% 1.54/1.73 (~r(s(s(z)), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2849, 189, 4156, 4222])).
% 1.54/1.73 tff(4224,plain,
% 1.54/1.73 (b(s(s(z)), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2301, 4223, 4103])).
% 1.54/1.73 tff(4225,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4226,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4227,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4226, 4225])).
% 1.54/1.73 tff(4228,plain,
% 1.54/1.73 (~r(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4227, 189, 1141, 4222])).
% 1.54/1.73 tff(4229,plain,
% 1.54/1.73 (b(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2228, 4228, 2224])).
% 1.54/1.73 tff(4230,plain,
% 1.54/1.73 (((~b(elem!1, s(z))) | (~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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4231,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4230])).
% 1.54/1.73 tff(4232,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4231, 2871])).
% 1.54/1.73 tff(4233,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4234,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 1.54/1.73 tff(4235,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4234, 337, 327, 791, 4229, 4224])).
% 1.54/1.73 tff(4236,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4237,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4236, 4221, 4103, 791, 327, 4193])).
% 1.54/1.73 tff(4238,plain,
% 1.54/1.73 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2268, 4237])).
% 1.54/1.73 tff(4239,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4240,plain,
% 1.54/1.73 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), 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))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4241,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4240])).
% 1.54/1.73 tff(4242,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4241, 4239])).
% 1.54/1.73 tff(4243,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4244,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 1.54/1.73 tff(4245,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4244, 337, 791, 1, 1301, 3864])).
% 1.54/1.73 tff(4246,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[851, 4245])).
% 1.54/1.73 tff(4247,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4248,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4249,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4248, 4247])).
% 1.54/1.73 tff(4250,plain,
% 1.54/1.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4249, 189, 4246, 118])).
% 1.54/1.73 tff(4251,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[524, 4250])).
% 1.54/1.73 tff(4252,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4253,plain,
% 1.54/1.73 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4254,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(X1, 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(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4253])).
% 1.54/1.73 tff(4255,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(X1, 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(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4254, 4252])).
% 1.54/1.73 tff(4256,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4257,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 1.54/1.73 tff(4258,plain,
% 1.54/1.73 (~b(s(s(z)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4257, 337, 4251, 4195, 4238, 2777])).
% 1.54/1.73 tff(4259,plain,
% 1.54/1.73 (r(s(s(z)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2242, 4258])).
% 1.54/1.73 tff(4260,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4261,plain,
% 1.54/1.73 (((~b(s(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(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(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)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4262,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4261])).
% 1.54/1.73 tff(4263,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4262, 4260])).
% 1.54/1.73 tff(4264,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4265,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 1.54/1.73 tff(4266,plain,
% 1.54/1.73 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4265, 337, 4251, 4195, 4238])).
% 1.54/1.73 tff(4267,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1298, 43])).
% 1.54/1.73 tff(4268,plain,
% 1.54/1.73 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4267, 2008])).
% 1.54/1.73 tff(4269,plain,
% 1.54/1.73 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4268, 4266])).
% 1.54/1.73 tff(4270,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4271,plain,
% 1.54/1.73 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4272,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4271])).
% 1.54/1.73 tff(4273,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4272, 4270])).
% 1.54/1.73 tff(4274,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4275,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4274, 4273])).
% 1.54/1.73 tff(4276,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4275, 189, 4269, 4259, 4204])).
% 1.54/1.73 tff(4277,plain,((~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4278,plain,
% 1.54/1.73 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4277, 4185, 4103, 327, 4102, 118, 1301, 1, 4101, 117, 4099])).
% 1.54/1.73 tff(4279,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[857, 4278, 853])).
% 1.54/1.73 tff(4280,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[864, 337, 327, 4185, 4279])).
% 1.54/1.73 tff(4281,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[851, 4280])).
% 1.54/1.73 tff(4282,plain,
% 1.54/1.73 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1570, 337, 327, 4185, 4279])).
% 1.54/1.73 tff(4283,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1150, 4282])).
% 1.54/1.73 tff(4284,plain,
% 1.54/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2027, 4283, 118])).
% 1.54/1.73 tff(4285,plain,
% 1.54/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[548, 4284])).
% 1.54/1.73 tff(4286,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1609, 337, 327, 791, 2, 1603, 2454])).
% 1.54/1.73 tff(4287,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4288,plain,
% 1.54/1.73 (~b(s(s(s(z))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4287, 327, 4185, 4285, 4279])).
% 1.54/1.73 tff(4289,plain,
% 1.54/1.73 (r(s(s(s(z))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2463, 4288, 117])).
% 1.54/1.73 tff(4290,plain,
% 1.54/1.73 (~r(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4211, 4289, 4101])).
% 1.54/1.73 tff(4291,plain,
% 1.54/1.73 (b(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1498, 4290])).
% 1.54/1.73 tff(4292,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4293,plain,
% 1.54/1.73 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4294,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(X1, 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(z))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4293])).
% 1.54/1.73 tff(4295,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(X1, 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(z))), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4294, 4292])).
% 1.54/1.74 tff(4296,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4297,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 1.54/1.74 tff(4298,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4297, 337, 1, 1301, 1659, 1658])).
% 1.54/1.74 tff(4299,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4300,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4299, 1659, 1301, 1])).
% 1.54/1.74 tff(4301,plain,
% 1.54/1.74 (r(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[46, 43, 33, 4300])).
% 1.54/1.74 tff(4302,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3611, 189, 811, 4301])).
% 1.54/1.74 tff(4303,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[548, 4302])).
% 1.54/1.74 tff(4304,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4249, 189, 811, 4301])).
% 1.54/1.74 tff(4305,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[524, 4304])).
% 1.54/1.74 tff(4306,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), 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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4307,plain,
% 1.54/1.74 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(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(s(s(z))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4308,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4307])).
% 1.54/1.74 tff(4309,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4308, 4306])).
% 1.54/1.74 tff(4310,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4311,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4310, 4309])).
% 1.54/1.74 tff(4312,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4311, 337, 4305, 4303, 1592, 1659])).
% 1.54/1.74 tff(4313,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4314,plain,
% 1.54/1.74 (~b(z, s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4313, 4291, 1301, 1, 4281])).
% 1.54/1.74 tff(4315,plain,
% 1.54/1.74 (r(z, s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1786, 4314])).
% 1.54/1.74 tff(4316,plain,
% 1.54/1.74 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4164, 4315, 4099])).
% 1.54/1.74 tff(4317,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4172, 4316, 83])).
% 1.54/1.74 tff(4318,plain,
% 1.54/1.74 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[700, 4317, 4091])).
% 1.54/1.74 tff(4319,plain,
% 1.54/1.74 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4318, 4086])).
% 1.54/1.74 tff(4320,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4249, 189, 4281, 118])).
% 1.54/1.74 tff(4321,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[524, 4320])).
% 1.54/1.74 tff(4322,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4323,plain,
% 1.54/1.74 (((~b(s(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(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4324,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4323])).
% 1.54/1.74 tff(4325,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4324, 4322])).
% 1.54/1.74 tff(4326,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4327,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 1.54/1.74 tff(4328,plain,
% 1.54/1.74 (~b(elem!1, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4327, 337, 4321, 4285, 4319])).
% 1.54/1.74 tff(4329,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4328, 4085])).
% 1.54/1.74 tff(4330,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3252, 4329])).
% 1.54/1.74 tff(4331,plain,
% 1.54/1.74 (r(elem!1, s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4330, 4084])).
% 1.54/1.74 tff(4332,plain,
% 1.54/1.74 (b(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2229, 4228])).
% 1.54/1.74 tff(4333,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4334,plain,
% 1.54/1.74 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4335,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4334])).
% 1.54/1.74 tff(4336,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4335, 4333])).
% 1.54/1.74 tff(4337,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4338,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4337, 4336])).
% 1.54/1.74 tff(4339,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4338, 189, 1115, 4222])).
% 1.54/1.74 tff(4340,plain,
% 1.54/1.74 (b(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2242, 4339])).
% 1.54/1.74 tff(4341,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4342,plain,
% 1.54/1.74 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4343,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4342])).
% 1.54/1.74 tff(4344,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4343, 4341])).
% 1.54/1.74 tff(4345,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4346,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 1.54/1.74 tff(4347,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4346, 337, 327, 791, 1301, 4340, 4332])).
% 1.54/1.74 tff(4348,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4349,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4348, 327, 4185, 1301, 4315, 4283])).
% 1.54/1.74 tff(4350,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2268, 4349])).
% 1.54/1.74 tff(4351,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4352,plain,
% 1.54/1.74 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(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(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4353,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4352])).
% 1.54/1.74 tff(4354,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4353, 4351])).
% 1.54/1.74 tff(4355,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4356,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 1.54/1.74 tff(4357,plain,
% 1.54/1.74 (~b(s(s(z)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4356, 337, 4321, 4285, 4350, 4319])).
% 1.54/1.74 tff(4358,plain,
% 1.54/1.74 (r(s(s(z)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2301, 4357, 4103])).
% 1.54/1.74 tff(4359,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4265, 337, 4321, 4285, 4350])).
% 1.54/1.74 tff(4360,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4268, 4359])).
% 1.54/1.74 tff(4361,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4362,plain,
% 1.54/1.74 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4363,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4362])).
% 1.54/1.74 tff(4364,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4363, 4361])).
% 1.54/1.74 tff(4365,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4366,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4365, 4364])).
% 1.54/1.74 tff(4367,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4366, 189, 4360, 4358, 4331])).
% 1.54/1.74 tff(4368,plain,((~b(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4369,plain,
% 1.54/1.75 (~b(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4368, 156, 3844, 83, 4083, 118, 171, 61])).
% 1.54/1.75 tff(4370,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.54/1.75 tff(4371,plain,
% 1.54/1.75 (r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[322, 4370, 3850])).
% 1.54/1.75 tff(4372,plain,
% 1.54/1.75 (~r(s(s(s(z))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3923, 189, 4371, 118])).
% 1.54/1.75 tff(4373,plain,
% 1.54/1.75 (b(s(s(s(z))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2463, 4372, 117])).
% 1.54/1.75 tff(4374,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4375,plain,
% 1.54/1.75 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4376,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4375])).
% 1.54/1.75 tff(4377,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4376, 4374])).
% 1.54/1.75 tff(4378,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4379,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 1.54/1.75 tff(4380,plain,
% 1.54/1.75 (~b(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4379, 337, 1763, 1, 1301])).
% 1.54/1.75 tff(4381,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.54/1.75 tff(4382,plain,
% 1.54/1.75 (b(z, elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[921, 2883, 65])).
% 1.54/1.75 tff(4383,plain,
% 1.54/1.75 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[928, 4382, 82])).
% 1.54/1.75 tff(4384,plain,
% 1.54/1.75 (r(s(elem!1), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[378, 43, 114, 1250])).
% 1.54/1.75 tff(4385,plain,
% 1.54/1.75 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1227, 4384, 215])).
% 1.54/1.75 tff(4386,plain,
% 1.54/1.75 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[63])).
% 1.54/1.75 tff(4387,plain,
% 1.54/1.75 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.54/1.75 inference(transitivity,[status(thm)],[4386, 70])).
% 1.54/1.75 tff(4388,plain,
% 1.54/1.75 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[4387])).
% 1.54/1.75 tff(4389,plain,
% 1.54/1.75 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[4388, 120])).
% 1.54/1.75 tff(4390,plain,
% 1.54/1.75 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4389])).
% 1.54/1.75 tff(4391,plain,
% 1.54/1.75 (~(s(z) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[74, 4390])).
% 1.54/1.75 tff(4392,plain,
% 1.54/1.75 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[63])).
% 1.54/1.75 tff(4393,plain,
% 1.54/1.75 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[4392])).
% 1.54/1.75 tff(4394,plain,
% 1.54/1.75 (z = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[67, 63])).
% 1.54/1.75 tff(4395,plain,
% 1.54/1.75 (s(elem!1) = s(z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[60, 4394])).
% 1.54/1.75 tff(4396,plain,
% 1.54/1.75 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4395])).
% 1.54/1.75 tff(4397,plain,
% 1.54/1.75 (r(s(elem!1), z) <=> r(s(z), elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[4396, 4393])).
% 1.54/1.75 tff(4398,plain,
% 1.54/1.75 ((~r(s(elem!1), z)) <=> (~r(s(z), elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4397])).
% 1.54/1.75 tff(4399,plain,
% 1.54/1.75 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[63])).
% 1.54/1.75 tff(4400,plain,
% 1.54/1.75 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4399])).
% 1.54/1.75 tff(4401,plain,
% 1.54/1.75 (~r(s(elem!1), z)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3062, 4400])).
% 1.54/1.75 tff(4402,plain,
% 1.54/1.75 (~r(s(z), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4401, 4398])).
% 1.54/1.75 tff(4403,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[727, 4402, 4391, 4381])).
% 1.54/1.75 tff(4404,plain,((~(elem!1 = z)) | b(s(z), elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4405,plain,
% 1.54/1.75 (~(elem!1 = z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4404, 4381, 3062])).
% 1.54/1.75 tff(4406,plain,
% 1.54/1.75 (r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[322, 247, 4370])).
% 1.54/1.75 tff(4407,plain,
% 1.54/1.75 (r(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[727, 272, 4381])).
% 1.54/1.75 tff(4408,plain,
% 1.54/1.75 ((z = elem!1) <=> (elem!1 = z)),
% 1.54/1.75 inference(symmetry,[status(thm)],[62])).
% 1.54/1.75 tff(4409,plain,
% 1.54/1.75 (elem!1 = z),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[56, 4408])).
% 1.54/1.75 tff(4410,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1900, 4409])).
% 1.54/1.75 tff(4411,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4412,plain,
% 1.54/1.75 (~(z = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4411, 1900])).
% 1.54/1.75 tff(4413,plain,
% 1.54/1.75 (~(s(elem!1) = s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3076, 4412])).
% 1.54/1.75 tff(4414,plain,
% 1.54/1.75 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[632, 282])).
% 1.54/1.75 tff(4415,plain,
% 1.54/1.75 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3955, 984, 3062, 4414])).
% 1.54/1.75 tff(4416,plain,
% 1.54/1.75 (~(s(elem!1) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[264, 4415])).
% 1.54/1.75 tff(4417,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[270, 4416, 3062])).
% 1.54/1.75 tff(4418,plain,
% 1.54/1.75 (~(elem!1 = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[980, 4416])).
% 1.54/1.75 tff(4419,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[350, 984, 276])).
% 1.54/1.75 tff(4420,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2153, 4419, 777])).
% 1.54/1.75 tff(4421,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[227, 43, 4420])).
% 1.54/1.75 tff(4422,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4421, 369])).
% 1.54/1.75 tff(4423,plain,
% 1.54/1.75 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2164, 189, 4419, 1735])).
% 1.54/1.75 tff(4424,plain,
% 1.54/1.75 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[310, 43, 211, 4423])).
% 1.54/1.75 tff(4425,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1082, 215, 1077])).
% 1.54/1.75 tff(4426,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[363, 4415, 4425])).
% 1.54/1.75 tff(4427,plain,
% 1.54/1.75 (~b(s(elem!1), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2144, 4426, 4424, 4422])).
% 1.54/1.75 tff(4428,plain,
% 1.54/1.75 (r(s(elem!1), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[898, 4427, 4413])).
% 1.54/1.75 tff(4429,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4430,plain,
% 1.54/1.75 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4431,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4430])).
% 1.54/1.75 tff(4432,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4431, 4429])).
% 1.54/1.75 tff(4433,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4434,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 1.54/1.75 tff(4435,plain,
% 1.54/1.75 (~r(elem!1, s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4434, 189, 777, 4428])).
% 1.54/1.75 tff(4436,plain,
% 1.54/1.75 (b(elem!1, s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1015, 4435, 4418])).
% 1.54/1.75 tff(4437,plain,
% 1.54/1.75 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2528, 337, 4426, 4417, 4436])).
% 1.54/1.75 tff(4438,plain,
% 1.54/1.75 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[295, 43, 282, 4437])).
% 1.54/1.75 tff(4439,plain,
% 1.54/1.75 (~r(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[291, 4438, 215])).
% 1.54/1.75 tff(4440,plain,
% 1.54/1.75 (b(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1759, 4439, 1900])).
% 1.54/1.75 tff(4441,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4442,plain,
% 1.54/1.75 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4443,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4442])).
% 1.54/1.75 tff(4444,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4443, 4441])).
% 1.54/1.75 tff(4445,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4446,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 1.54/1.75 tff(4447,plain,
% 1.54/1.75 (~r(z, elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4446, 189, 4438, 215])).
% 1.54/1.75 tff(4448,plain,
% 1.54/1.75 (b(z, elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[921, 4447, 4412])).
% 1.54/1.75 tff(4449,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.54/1.75 tff(4450,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, 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, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4451,plain,
% 1.54/1.75 (((~b(z, elem!1)) | (~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(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4452,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4451])).
% 1.54/1.75 tff(4453,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4452, 4450])).
% 1.54/1.75 tff(4454,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4455,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4454, 4453])).
% 1.54/1.75 tff(4456,plain,
% 1.54/1.75 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4455, 337, 925, 1763, 4449])).
% 1.54/1.75 tff(4457,plain,
% 1.54/1.75 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[663, 4456])).
% 1.54/1.75 tff(4458,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4459,plain,
% 1.54/1.75 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4460,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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)))), s(elem!1)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4459])).
% 1.54/1.75 tff(4461,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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)))), s(elem!1))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4460, 4458])).
% 1.54/1.75 tff(4462,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4463,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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)))), s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4462, 4461])).
% 1.54/1.75 tff(4464,plain,
% 1.54/1.75 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4463, 337, 925, 1763, 2520, 4449])).
% 1.54/1.75 tff(4465,plain,
% 1.54/1.75 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[649, 4464, 3949])).
% 1.54/1.75 tff(4466,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4467,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4468,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4467, 4466])).
% 1.54/1.75 tff(4469,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4468, 189, 1219, 4465, 4457])).
% 1.54/1.75 tff(4470,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), z)) | (s(s(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,[]))).
% 1.54/1.75 tff(4471,plain,
% 1.54/1.75 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4470, 4384, 4414, 4448, 4440, 4417])).
% 1.54/1.75 tff(4472,plain,
% 1.54/1.75 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[427, 4415])).
% 1.54/1.75 tff(4473,plain,
% 1.54/1.75 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[579, 4385, 4472])).
% 1.54/1.75 tff(4474,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4475,plain,
% 1.54/1.75 (((~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))) | (~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(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4476,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4475])).
% 1.54/1.75 tff(4477,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4476, 4474])).
% 1.54/1.75 tff(4478,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4479,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4478, 4477])).
% 1.54/1.75 tff(4480,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4479, 337, 365, 638, 4026, 241, 4018])).
% 1.54/1.75 tff(4481,plain,((~r(s(z), z)) | (~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(z))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4482,plain,
% 1.54/1.75 (~r(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4481, 4473, 4426, 4422, 4413, 4384])).
% 1.54/1.75 tff(4483,plain,
% 1.54/1.75 (b(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[963, 4482])).
% 1.54/1.75 tff(4484,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), 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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4485,plain,
% 1.54/1.76 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), 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(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4486,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4485])).
% 1.54/1.76 tff(4487,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4486, 4484])).
% 1.54/1.76 tff(4488,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4489,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4488, 4487])).
% 1.54/1.76 tff(4490,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4489, 337, 4448, 4426, 4483, 4436, 4424])).
% 1.54/1.76 tff(4491,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[406, 43, 133, 4490])).
% 1.54/1.76 tff(4492,plain,
% 1.54/1.76 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3128, 4415])).
% 1.54/1.76 tff(4493,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[678, 189, 2177, 3276])).
% 1.54/1.76 tff(4494,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(4495,plain,
% 1.54/1.76 (((~![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)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4496,plain,
% 1.54/1.76 ((~![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)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4497,plain,
% 1.54/1.76 ((~![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))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 1.54/1.76 tff(4498,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4497, 43, 4494, 4493])).
% 1.54/1.76 tff(4499,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4468, 189, 1219, 3276])).
% 1.54/1.76 tff(4500,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[649, 4499, 3949])).
% 1.54/1.76 tff(4501,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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(elem!1, 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))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4502,plain,
% 1.54/1.76 (((~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))), 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4503,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1, 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)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4502])).
% 1.54/1.76 tff(4504,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1, 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))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4503, 4501])).
% 1.54/1.76 tff(4505,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4506,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4505, 4504])).
% 1.54/1.76 tff(4507,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4506, 337, 365, 2520, 982, 4500, 4498])).
% 1.54/1.76 tff(4508,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4509,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4508, 4426, 4417, 4436, 4492, 4414, 4491, 4384])).
% 1.54/1.76 tff(4510,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[663, 4509])).
% 1.54/1.76 tff(4511,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, 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(X1, 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(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4512,plain,
% 1.54/1.76 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4513,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4512])).
% 1.54/1.76 tff(4514,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4513, 4511])).
% 1.54/1.76 tff(4515,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4516,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4515, 4514])).
% 1.54/1.76 tff(4517,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4516, 337, 4448, 4440, 4483, 4510])).
% 1.54/1.76 tff(4518,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4519,plain,
% 1.54/1.76 ((~![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)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4520,plain,
% 1.54/1.76 ((~![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))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 1.54/1.76 tff(4521,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4520, 43, 135, 4517])).
% 1.54/1.76 tff(4522,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4523,plain,
% 1.54/1.76 (((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4524,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4523])).
% 1.54/1.76 tff(4525,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4524, 4522])).
% 1.54/1.76 tff(4526,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4527,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.54/1.76 tff(4528,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4527, 189, 777, 4521])).
% 1.54/1.76 tff(4529,plain,
% 1.54/1.76 (s(s(s(s(elem!1)))) = elem!1),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[714, 4528, 4471])).
% 1.54/1.76 tff(4530,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.54/1.76 tff(4531,plain,
% 1.54/1.76 (elem!1 = s(s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4530])).
% 1.54/1.76 tff(4532,plain,
% 1.54/1.76 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[157, 4531])).
% 1.54/1.76 tff(4533,plain,
% 1.54/1.76 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4532])).
% 1.54/1.76 tff(4534,plain,
% 1.54/1.76 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[162, 4533, 98])).
% 1.54/1.76 tff(4535,plain,
% 1.54/1.76 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4534])).
% 1.54/1.76 tff(4536,plain,
% 1.54/1.76 (s(s(z)) = s(s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[21, 4535, 87])).
% 1.54/1.76 tff(4537,plain,
% 1.54/1.76 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4536])).
% 1.54/1.76 tff(4538,plain,
% 1.54/1.76 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4537])).
% 1.54/1.76 tff(4539,plain,
% 1.54/1.76 (s(elem!1) = s(z)),
% 1.54/1.76 inference(transitivity,[status(thm)],[111, 4538, 104])).
% 1.54/1.76 tff(4540,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[50, 4539])).
% 1.54/1.76 tff(4541,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4542,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4541, 4529, 4413])).
% 1.54/1.76 tff(4543,plain,
% 1.54/1.76 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[162, 2735, 91, 4531])).
% 1.54/1.76 tff(4544,plain,
% 1.54/1.76 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4543])).
% 1.54/1.76 tff(4545,plain,
% 1.54/1.76 (s(s(z)) = s(s(s(elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[21, 4544, 98])).
% 1.54/1.76 tff(4546,plain,
% 1.54/1.76 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4545])).
% 1.54/1.76 tff(4547,plain,
% 1.54/1.76 (s(z) = s(s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[105, 4546, 87])).
% 1.54/1.76 tff(4548,plain,
% 1.54/1.76 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4547])).
% 1.54/1.76 tff(4549,plain,
% 1.54/1.76 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4548])).
% 1.54/1.76 tff(4550,plain,
% 1.54/1.76 (s(elem!1) = z),
% 1.54/1.76 inference(transitivity,[status(thm)],[111, 4549, 14])).
% 1.54/1.76 tff(4551,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[114, 4550])).
% 1.54/1.76 tff(4552,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4553,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4552, 4529])).
% 1.54/1.76 tff(4554,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3992, 4384, 4553, 4448, 4440, 4417])).
% 1.54/1.76 tff(4555,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[857, 4554, 4542])).
% 1.54/1.76 tff(4556,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4557,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4558,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4557, 4556])).
% 1.54/1.76 tff(4559,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4558, 189, 4419, 4555])).
% 1.54/1.76 tff(4560,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(4561,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1947, 43, 4560, 4559])).
% 1.54/1.76 tff(4562,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2079, 189, 1735, 4555])).
% 1.54/1.76 tff(4563,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[851, 4562])).
% 1.54/1.76 tff(4564,plain,
% 1.54/1.76 (~(s(z) = s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4413, 4011])).
% 1.54/1.76 tff(4565,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4566,plain,
% 1.54/1.76 (((~b(s(elem!1), elem!1)) | (~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(z), s(s(s(elem!1))))) | (~b(s(z), 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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4567,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4566])).
% 1.54/1.76 tff(4568,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4567, 4565])).
% 1.54/1.76 tff(4569,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4570,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 1.54/1.76 tff(4571,plain,
% 1.54/1.76 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4570, 337, 4426, 4417, 4424])).
% 1.54/1.76 tff(4572,plain,
% 1.54/1.76 (~b(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4571, 4473])).
% 1.54/1.76 tff(4573,plain,
% 1.54/1.76 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2133, 43, 4572])).
% 1.54/1.76 tff(4574,plain,
% 1.54/1.76 (r(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4573, 4564])).
% 1.54/1.76 tff(4575,plain,
% 1.54/1.76 (~r(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2705, 189, 1077, 4574])).
% 1.54/1.76 tff(4576,plain,
% 1.54/1.76 (b(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[80, 4575])).
% 1.54/1.76 tff(4577,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4578,plain,
% 1.54/1.76 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~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)))))) <=> ((~b(s(z), z)) | (~b(z, 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))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4579,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4578])).
% 1.54/1.76 tff(4580,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4579, 4577])).
% 1.54/1.76 tff(4581,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4582,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4581, 4580])).
% 1.54/1.76 tff(4583,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4582, 337, 4483, 4576, 4563, 4422, 4561])).
% 1.54/1.76 tff(4584,plain,(b(s(s(s(elem!1))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | b(s(elem!1), z) | (elem!1 = z) | r(s(elem!1), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4585,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4584, 215, 4407, 4406, 1077, 2518, 1250, 4405, 3062, 276])).
% 1.54/1.76 tff(4586,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2743, 83, 247])).
% 1.54/1.76 tff(4587,plain,
% 1.54/1.76 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[975])).
% 1.54/1.76 tff(4588,plain,
% 1.54/1.76 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[83])).
% 1.54/1.76 tff(4589,plain,
% 1.54/1.76 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[4588, 975])).
% 1.54/1.76 tff(4590,plain,
% 1.54/1.76 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4589, 4587])).
% 1.54/1.76 tff(4591,plain,
% 1.54/1.76 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(elem!1 = s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4590])).
% 1.54/1.76 tff(4592,plain,
% 1.54/1.76 (~(elem!1 = s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[630, 4591])).
% 1.54/1.76 tff(4593,plain,
% 1.54/1.76 (b(s(elem!1), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[326, 2909])).
% 1.54/1.76 tff(4594,plain,
% 1.54/1.76 (~r(z, elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[785, 173, 777])).
% 1.54/1.77 tff(4595,plain,
% 1.54/1.77 (b(z, elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[921, 4594, 4412])).
% 1.54/1.77 tff(4596,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[170, 83, 4413])).
% 1.54/1.77 tff(4597,plain,
% 1.54/1.77 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4596, 4090])).
% 1.54/1.77 tff(4598,plain,
% 1.54/1.77 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2502])).
% 1.54/1.77 tff(4599,plain,
% 1.54/1.77 (s(s(s(s(z)))) = elem!1),
% 1.54/1.77 inference(transitivity,[status(thm)],[4598, 121, 88, 91])).
% 1.54/1.77 tff(4600,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[853, 4599])).
% 1.54/1.77 tff(4601,plain,((~(s(s(s(z))) = s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4602,plain,
% 1.54/1.77 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4601, 4596, 83])).
% 1.54/1.77 tff(4603,plain,
% 1.54/1.77 (~r(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1707, 189, 777, 173])).
% 1.54/1.77 tff(4604,plain,
% 1.54/1.77 (b(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1759, 4603, 1900])).
% 1.54/1.77 tff(4605,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3992, 4604, 1219, 829, 4595, 2520])).
% 1.54/1.77 tff(4606,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[857, 4605, 4596])).
% 1.54/1.77 tff(4607,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2079, 189, 1735, 4606])).
% 1.54/1.77 tff(4608,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[851, 4607])).
% 1.54/1.77 tff(4609,plain,
% 1.54/1.77 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2089, 4606, 1735])).
% 1.54/1.77 tff(4610,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1150, 4609])).
% 1.54/1.77 tff(4611,plain,
% 1.54/1.77 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[93])).
% 1.54/1.77 tff(4612,plain,
% 1.54/1.77 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4611])).
% 1.54/1.77 tff(4613,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2107, 337, 1544, 1275, 1231])).
% 1.54/1.77 tff(4614,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[832, 43, 829, 4613])).
% 1.54/1.77 tff(4615,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2966, 189, 1077, 4614])).
% 1.54/1.77 tff(4616,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[820, 43, 817, 4615])).
% 1.54/1.77 tff(4617,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4618,plain,
% 1.54/1.77 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4619,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4618])).
% 1.54/1.77 tff(4620,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4619, 4617])).
% 1.54/1.77 tff(4621,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4622,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 1.54/1.77 tff(4623,plain,
% 1.54/1.77 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4622, 337, 925, 1763, 4616])).
% 1.54/1.77 tff(4624,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4623, 4612])).
% 1.54/1.77 tff(4625,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[700, 4624, 3466])).
% 1.54/1.77 tff(4626,plain,
% 1.54/1.77 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4172, 4625, 83])).
% 1.54/1.77 tff(4627,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(4628,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4627])).
% 1.54/1.77 tff(4629,plain,
% 1.54/1.77 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4628])).
% 1.54/1.77 tff(4630,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[829, 4629])).
% 1.54/1.77 tff(4631,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4632,plain,
% 1.54/1.77 (((~b(s(s(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(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4633,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4632])).
% 1.54/1.77 tff(4634,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4633, 4631])).
% 1.54/1.77 tff(4635,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4636,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 1.54/1.77 tff(4637,plain,
% 1.54/1.77 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4636, 337, 1544, 1275, 1231])).
% 1.54/1.77 tff(4638,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4639,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4640,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 1.54/1.77 tff(4641,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4640, 43, 4637])).
% 1.54/1.77 tff(4642,plain,
% 1.54/1.77 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4641, 4630])).
% 1.54/1.77 tff(4643,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.54/1.77 tff(4644,plain,
% 1.54/1.77 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[94])).
% 1.54/1.77 tff(4645,plain,
% 1.54/1.77 (~(s(s(s(z))) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1472, 829])).
% 1.54/1.77 tff(4646,plain,
% 1.54/1.77 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4645, 4644])).
% 1.54/1.77 tff(4647,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4648,plain,
% 1.54/1.77 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4649,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4648])).
% 1.54/1.77 tff(4650,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4649, 4647])).
% 1.54/1.77 tff(4651,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4652,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.54/1.77 tff(4653,plain,
% 1.54/1.77 (~r(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4652, 189, 4626, 4642])).
% 1.54/1.77 tff(4654,plain,
% 1.54/1.77 (b(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1015, 4653, 1008])).
% 1.54/1.77 tff(4655,plain,
% 1.54/1.77 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[93])).
% 1.54/1.77 tff(4656,plain,
% 1.54/1.77 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[4655])).
% 1.54/1.77 tff(4657,plain,
% 1.54/1.77 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[93])).
% 1.54/1.77 tff(4658,plain,
% 1.54/1.77 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4657])).
% 1.54/1.77 tff(4659,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4660,plain,
% 1.54/1.77 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4661,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4660])).
% 1.54/1.77 tff(4662,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4661, 4659])).
% 1.54/1.77 tff(4663,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4664,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4663, 4662])).
% 1.54/1.77 tff(4665,plain,
% 1.54/1.77 (~r(s(s(s(z))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4664, 189, 1339, 4156])).
% 1.54/1.77 tff(4666,plain,
% 1.54/1.77 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4665, 4658])).
% 1.54/1.77 tff(4667,plain,
% 1.54/1.77 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1820, 4666, 692])).
% 1.54/1.77 tff(4668,plain,
% 1.54/1.77 (b(s(s(s(z))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4667, 4656])).
% 1.54/1.77 tff(4669,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4670,plain,
% 1.54/1.77 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4671,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4670])).
% 1.54/1.77 tff(4672,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4671, 4669])).
% 1.54/1.77 tff(4673,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4674,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 1.54/1.77 tff(4675,plain,
% 1.54/1.77 (~r(s(s(s(z))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4674, 189, 1339, 3559])).
% 1.54/1.77 tff(4676,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4677,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4678,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4677, 4676])).
% 1.54/1.77 tff(4679,plain,
% 1.54/1.77 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 4675])).
% 1.54/1.77 tff(4680,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4681,plain,
% 1.54/1.77 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4682,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4681])).
% 1.54/1.77 tff(4683,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4682, 4680])).
% 1.54/1.77 tff(4684,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4685,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4684, 4683])).
% 1.54/1.78 tff(4686,plain,
% 1.54/1.78 (~b(s(s(s(z))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4685, 337, 1763, 2520, 982, 4679])).
% 1.54/1.78 tff(4687,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4686, 4668])).
% 1.54/1.78 tff(4688,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (s(s(s(z))) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4689,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4688, 4654, 1763, 2520, 83, 4646, 4643, 4642, 4626])).
% 1.54/1.78 tff(4690,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[548, 4689])).
% 1.54/1.78 tff(4691,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1281, 337, 1275, 4690, 1231])).
% 1.54/1.78 tff(4692,plain,
% 1.54/1.78 (r(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[48, 4691])).
% 1.54/1.78 tff(4693,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4694,plain,
% 1.54/1.78 (((~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))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4695,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4694])).
% 1.54/1.78 tff(4696,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4695, 4693])).
% 1.54/1.78 tff(4697,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4698,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 1.54/1.78 tff(4699,plain,
% 1.54/1.78 (~r(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4698, 189, 1077, 4614])).
% 1.54/1.78 tff(4700,plain,
% 1.54/1.78 (b(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1584, 43, 4699, 1562])).
% 1.54/1.78 tff(4701,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(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)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(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)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4702,plain,
% 1.54/1.78 (((~b(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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(s(s(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)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4703,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(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)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4702])).
% 1.54/1.78 tff(4704,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(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)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4703, 4701])).
% 1.54/1.78 tff(4705,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4706,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 1.54/1.78 tff(4707,plain,
% 1.54/1.78 (~b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4706, 337, 1275, 4690, 1231, 4700])).
% 1.54/1.78 tff(4708,plain,
% 1.54/1.78 (r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1498, 4707])).
% 1.54/1.78 tff(4709,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1766, 189, 173, 4708, 4692])).
% 1.54/1.78 tff(4710,plain,((~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (elem!1 = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(z, elem!1)) | (~r(z, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4711,plain,
% 1.54/1.78 (~b(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4710, 173, 4610, 4608, 4604, 2520, 83, 4602, 1008, 4597, 4595, 1077, 829])).
% 1.54/1.78 tff(4712,plain,
% 1.54/1.78 (r(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[898, 4711, 4413])).
% 1.54/1.78 tff(4713,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2381, 189, 1219, 4712, 173])).
% 1.54/1.78 tff(4714,plain,((~r(z, s(z))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(elem!1)) | (~r(z, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(z), elem!1)) | (elem!1 = z) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4715,plain,
% 1.54/1.78 (~r(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4714, 4593, 1219, 83, 4592, 1077, 4586, 4407, 4405, 4406])).
% 1.54/1.78 tff(4716,plain,
% 1.54/1.78 (b(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[80, 4715])).
% 1.54/1.78 tff(4717,plain,
% 1.54/1.78 (~(z = elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4411, 4405])).
% 1.54/1.78 tff(4718,plain,
% 1.54/1.78 (~(s(elem!1) = s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3076, 4717])).
% 1.54/1.78 tff(4719,plain,
% 1.54/1.78 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[170, 83, 4718])).
% 1.54/1.78 tff(4720,plain,
% 1.54/1.78 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4719, 4090])).
% 1.54/1.78 tff(4721,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4119, 370, 1735])).
% 1.54/1.78 tff(4722,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[857, 4721, 853])).
% 1.54/1.78 tff(4723,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4724,plain,
% 1.54/1.78 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4725,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4724])).
% 1.54/1.78 tff(4726,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4725, 4723])).
% 1.54/1.78 tff(4727,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4728,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4727, 4726])).
% 1.54/1.78 tff(4729,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4728, 189, 777, 811, 4156])).
% 1.54/1.78 tff(4730,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4731,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4730, 4156, 777])).
% 1.54/1.78 tff(4732,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[851, 4731])).
% 1.54/1.78 tff(4733,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4734,plain,
% 1.54/1.78 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4735,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4734])).
% 1.54/1.78 tff(4736,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4735, 4733])).
% 1.54/1.78 tff(4737,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4738,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4737, 4736])).
% 1.54/1.78 tff(4739,plain,
% 1.54/1.78 (~b(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4738, 337, 1, 1301, 4732])).
% 1.54/1.78 tff(4740,plain,
% 1.54/1.78 (r(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1584, 43, 4739, 1562])).
% 1.54/1.78 tff(4741,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4742,plain,
% 1.54/1.78 (((~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(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4743,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4742])).
% 1.54/1.78 tff(4744,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4743, 4741])).
% 1.54/1.78 tff(4745,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4746,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4745, 4744])).
% 1.54/1.78 tff(4747,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4746, 189, 370, 4740, 4156])).
% 1.54/1.78 tff(4748,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4749,plain,
% 1.54/1.78 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4748, 4111, 1301, 370, 777])).
% 1.54/1.78 tff(4750,plain,
% 1.54/1.78 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4172, 4749, 83])).
% 1.54/1.78 tff(4751,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[700, 4750, 4091])).
% 1.54/1.78 tff(4752,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4611])).
% 1.54/1.78 tff(4753,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(4754,plain,
% 1.54/1.78 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4753, 4752])).
% 1.54/1.78 tff(4755,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.54/1.78 tff(4756,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4757,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), 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(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4758,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4757])).
% 1.54/1.78 tff(4759,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4758, 4756])).
% 1.54/1.78 tff(4760,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4761,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4760, 4759])).
% 1.54/1.78 tff(4762,plain,
% 1.54/1.78 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4761, 337, 2520, 1603, 4755])).
% 1.54/1.78 tff(4763,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4762, 4754])).
% 1.54/1.78 tff(4764,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~(s(s(s(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)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4765,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4764, 4751, 2520, 4722, 83])).
% 1.54/1.78 tff(4766,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[832, 43, 829, 4765])).
% 1.54/1.78 tff(4767,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4117, 337, 4111, 1301, 1231])).
% 1.54/1.78 tff(4768,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[820, 43, 817, 4767])).
% 1.54/1.78 tff(4769,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3990, 189, 1219, 4768, 4766])).
% 1.54/1.78 tff(4770,plain,((~r(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4771,plain,
% 1.54/1.78 (~r(z, elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4770, 1231, 829, 1301, 1219, 2520, 83, 777, 4719, 1735])).
% 1.54/1.78 tff(4772,plain,
% 1.54/1.78 (b(z, elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[921, 4771, 4717])).
% 1.54/1.78 tff(4773,plain,
% 1.54/1.78 (~r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4044, 1231, 829, 2520, 1219, 4772, 1301, 4718])).
% 1.54/1.78 tff(4774,plain,
% 1.54/1.78 (b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[963, 4773])).
% 1.54/1.78 tff(4775,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4776,plain,
% 1.54/1.78 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4777,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4776])).
% 1.54/1.78 tff(4778,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4777, 4775])).
% 1.54/1.78 tff(4779,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4780,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4779, 4778])).
% 1.54/1.78 tff(4781,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4780, 337, 4772, 4774, 1301, 1231])).
% 1.54/1.78 tff(4782,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[820, 43, 817, 4781])).
% 1.54/1.78 tff(4783,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3990, 189, 1219, 4782])).
% 1.54/1.79 tff(4784,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[832, 43, 829, 4783])).
% 1.54/1.79 tff(4785,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4786,plain,
% 1.54/1.79 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~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(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4787,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4786])).
% 1.54/1.79 tff(4788,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4787, 4785])).
% 1.54/1.79 tff(4789,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4790,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, 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)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 1.54/1.79 tff(4791,plain,
% 1.54/1.79 ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4790, 337, 4772, 2520, 4774, 1231])).
% 1.54/1.79 tff(4792,plain,
% 1.54/1.79 (~b(s(elem!1), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4791, 4784])).
% 1.54/1.79 tff(4793,plain,
% 1.54/1.79 (r(s(elem!1), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[898, 4792, 4718])).
% 1.54/1.79 tff(4794,plain,
% 1.54/1.79 (~r(elem!1, s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4434, 189, 777, 4793])).
% 1.54/1.79 tff(4795,plain,
% 1.54/1.79 (b(elem!1, s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1015, 4794, 1008])).
% 1.54/1.79 tff(4796,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4797,plain,
% 1.54/1.79 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4798,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, 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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4797])).
% 1.54/1.79 tff(4799,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, 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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4798, 4796])).
% 1.54/1.79 tff(4800,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4801,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 1.54/1.79 tff(4802,plain,
% 1.54/1.79 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4801, 337, 2520, 4795, 4784])).
% 1.54/1.79 tff(4803,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4802, 4612])).
% 1.54/1.79 tff(4804,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[700, 4803, 4720])).
% 1.54/1.79 tff(4805,plain,
% 1.54/1.79 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4172, 4804, 83])).
% 1.54/1.79 tff(4806,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4807,plain,
% 1.54/1.79 (((~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(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4808,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4807])).
% 1.54/1.79 tff(4809,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4808, 4806])).
% 1.54/1.79 tff(4810,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4811,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 1.54/1.79 tff(4812,plain,
% 1.54/1.79 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4811, 189, 1219, 4782])).
% 1.54/1.79 tff(4813,plain,
% 1.54/1.79 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4640, 43, 4812])).
% 1.54/1.79 tff(4814,plain,
% 1.54/1.79 (b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4813, 4630])).
% 1.54/1.79 tff(4815,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4816,plain,
% 1.54/1.79 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(elem!1), 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))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4817,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~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(X1, 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(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4816])).
% 1.54/1.79 tff(4818,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~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(X1, 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(s(s(s(z)))), s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4817, 4815])).
% 1.54/1.79 tff(4819,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4820,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4819, 4818])).
% 1.54/1.79 tff(4821,plain,
% 1.54/1.79 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4820, 337, 2520, 4795, 4784])).
% 1.54/1.79 tff(4822,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[857, 4821, 4719])).
% 1.54/1.79 tff(4823,plain,
% 1.54/1.79 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2089, 4822, 1735])).
% 1.54/1.79 tff(4824,plain,
% 1.54/1.79 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1150, 4823])).
% 1.54/1.79 tff(4825,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4601, 4719, 83])).
% 1.54/1.79 tff(4826,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(4827,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4828,plain,
% 1.54/1.79 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4829,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4828])).
% 1.54/1.79 tff(4830,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4829, 4827])).
% 1.54/1.79 tff(4831,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4832,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4831, 4830])).
% 1.54/1.79 tff(4833,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4832, 337, 1275, 2, 1231, 4826])).
% 1.54/1.79 tff(4834,plain,
% 1.54/1.79 (r(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 4833])).
% 1.54/1.79 tff(4835,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4836,plain,
% 1.54/1.79 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4837,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4836])).
% 1.54/1.79 tff(4838,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4837, 4835])).
% 1.54/1.79 tff(4839,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4840,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4839, 4838])).
% 1.54/1.79 tff(4841,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4840, 337, 1, 1275, 2, 1231])).
% 1.54/1.79 tff(4842,plain,
% 1.54/1.79 (r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[48, 4841])).
% 1.54/1.79 tff(4843,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4844,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4845,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 1.54/1.79 tff(4846,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4845, 189, 788, 4842, 4834])).
% 1.54/1.79 tff(4847,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (s(s(s(z))) = s(elem!1)) | (~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(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4848,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4847, 4793, 4825, 4824, 1231, 4814, 4774])).
% 1.54/1.79 tff(4849,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[548, 4848])).
% 1.54/1.79 tff(4850,plain,
% 1.54/1.79 (~r(s(s(s(z))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4664, 189, 4849, 4805])).
% 1.54/1.79 tff(4851,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4850, 4658])).
% 1.54/1.79 tff(4852,plain,
% 1.54/1.79 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1820, 4851, 4646])).
% 1.54/1.79 tff(4853,plain,
% 1.54/1.79 (b(s(s(s(z))), elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4852, 4656])).
% 1.54/1.79 tff(4854,plain,
% 1.54/1.79 (~b(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4738, 337, 4774, 1301, 1231])).
% 1.54/1.79 tff(4855,plain,
% 1.54/1.79 (r(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1584, 43, 4854, 1562])).
% 1.54/1.79 tff(4856,plain,
% 1.54/1.79 (~r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1333, 189, 4849, 4855])).
% 1.54/1.79 tff(4857,plain,
% 1.54/1.79 (b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1498, 4856])).
% 1.54/1.79 tff(4858,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.54/1.79 tff(4859,plain,
% 1.54/1.79 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[63])).
% 1.54/1.79 tff(4860,plain,
% 1.54/1.79 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[4859])).
% 1.54/1.79 tff(4861,plain,
% 1.54/1.79 (b(elem!1, s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1301, 4860])).
% 1.54/1.79 tff(4862,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4370, 4861])).
% 1.54/1.79 tff(4863,plain,((~(elem!1 = z)) | b(elem!1, s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4864,plain,
% 1.54/1.79 (~(elem!1 = z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4863, 1301, 4370])).
% 1.54/1.79 tff(4865,plain,
% 1.54/1.79 (r(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1759, 4864, 4858])).
% 1.54/1.79 tff(4866,plain,
% 1.54/1.79 (~r(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1177, 4865, 1169])).
% 1.54/1.79 tff(4867,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[820, 43, 817, 4866])).
% 1.54/1.79 tff(4868,plain,
% 1.54/1.79 ((~(elem!1 = z)) <=> (~(z = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[62])).
% 1.54/1.79 tff(4869,plain,
% 1.54/1.79 (~(z = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4864, 4868])).
% 1.54/1.79 tff(4870,plain,
% 1.54/1.79 (~(s(elem!1) = s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3076, 4869])).
% 1.54/1.79 tff(4871,plain,
% 1.54/1.79 (b(z, elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[921, 4869, 2883])).
% 1.54/1.79 tff(4872,plain,
% 1.54/1.79 (s(z) = elem!1),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[727, 417, 4381])).
% 1.54/1.79 tff(4873,plain,
% 1.54/1.79 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4872])).
% 1.54/1.79 tff(4874,plain,
% 1.54/1.79 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4873, 4587])).
% 1.54/1.79 tff(4875,plain,
% 1.54/1.79 ((~(s(elem!1) = s(z))) <=> (~(elem!1 = s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4874])).
% 1.54/1.79 tff(4876,plain,
% 1.54/1.79 (~(elem!1 = s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[50, 4875])).
% 1.54/1.79 tff(4877,plain,
% 1.54/1.79 ((~(s(elem!1) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4873])).
% 1.54/1.79 tff(4878,plain,
% 1.54/1.79 (~(s(elem!1) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[50, 4877])).
% 1.54/1.79 tff(4879,plain,
% 1.54/1.79 (b(s(elem!1), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[270, 4878, 3062])).
% 1.54/1.79 tff(4880,plain,
% 1.54/1.79 (s(s(z)) = s(elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4872])).
% 1.54/1.79 tff(4881,plain,
% 1.54/1.79 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4880])).
% 1.54/1.79 tff(4882,plain,
% 1.54/1.79 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4881])).
% 1.54/1.79 tff(4883,plain,
% 1.54/1.80 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4882])).
% 1.54/1.80 tff(4884,plain,
% 1.54/1.80 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4883])).
% 1.54/1.80 tff(4885,plain,
% 1.54/1.80 (~b(z, s(s(s(elem!1))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[1784, 4884])).
% 1.54/1.80 tff(4886,plain,
% 1.54/1.80 (r(z, s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[146, 4885])).
% 1.54/1.80 tff(4887,plain,
% 1.54/1.80 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4882])).
% 1.54/1.80 tff(4888,plain,
% 1.54/1.80 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4887])).
% 1.54/1.80 tff(4889,plain,
% 1.54/1.80 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[229, 4888])).
% 1.54/1.80 tff(4890,plain,
% 1.54/1.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2913, 4889, 4879])).
% 1.54/1.80 tff(4891,plain,
% 1.54/1.80 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4872, 4882])).
% 1.54/1.80 tff(4892,plain,
% 1.54/1.80 (elem!1 = s(z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[322, 318, 4370])).
% 1.54/1.80 tff(4893,plain,
% 1.54/1.80 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[291, 4886, 274])).
% 1.54/1.80 tff(4894,plain,
% 1.54/1.80 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1144, 4893, 4892])).
% 1.54/1.80 tff(4895,plain,
% 1.54/1.80 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1150, 4894])).
% 1.54/1.80 tff(4896,plain,
% 1.54/1.80 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[4895, 4891])).
% 1.54/1.80 tff(4897,plain,
% 1.54/1.80 (~r(z, s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2530, 4879, 4896, 4890, 4876, 4886, 274])).
% 1.54/1.80 tff(4898,plain,
% 1.54/1.80 (b(z, s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[395, 4897])).
% 1.54/1.80 tff(4899,plain,
% 1.54/1.80 (~b(elem!1, s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2540, 4898, 4879, 925])).
% 1.54/1.80 tff(4900,plain,
% 1.54/1.80 (r(elem!1, s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1015, 4899, 4876])).
% 1.54/1.80 tff(4901,plain,
% 1.54/1.80 (~r(s(elem!1), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1023, 4900, 274])).
% 1.54/1.80 tff(4902,plain,
% 1.54/1.80 (b(s(elem!1), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[378, 43, 114, 4901])).
% 1.54/1.80 tff(4903,plain,
% 1.54/1.80 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4882])).
% 1.54/1.80 tff(4904,plain,
% 1.54/1.80 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[1169, 4903])).
% 1.54/1.80 tff(4905,plain,
% 1.54/1.80 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2551, 4900, 4904])).
% 1.54/1.80 tff(4906,plain,
% 1.54/1.80 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[363, 4905, 4890])).
% 1.54/1.80 tff(4907,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2559, 337, 925, 4906, 4898, 4879, 4896, 4902])).
% 1.54/1.80 tff(4908,plain,((~r(s(z), z)) | (~b(z, elem!1)) | (~r(elem!1, z)) | r(s(elem!1), elem!1) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), elem!1) | (s(elem!1) = s(z)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.80 tff(4909,plain,
% 1.54/1.80 (~r(s(z), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4908, 4871, 4865, 3062, 1784, 1169, 229, 4870, 4370, 4381])).
% 1.54/1.80 tff(4910,plain,
% 1.54/1.80 (b(s(z), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[963, 4909])).
% 1.54/1.80 tff(4911,plain,
% 1.54/1.80 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4191, 337, 4910, 1301, 4867])).
% 1.54/1.80 tff(4912,plain,
% 1.54/1.80 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1150, 4911])).
% 1.54/1.80 tff(4913,plain,
% 1.54/1.80 (~r(s(z), elem!1)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2089, 4912, 1169])).
% 1.54/1.80 tff(4914,plain,
% 1.54/1.80 (s(z) = elem!1),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[727, 4913, 4381])).
% 1.54/1.80 tff(4915,plain,
% 1.54/1.80 (b(s(z), z) <=> b(elem!1, z)),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4914])).
% 1.54/1.80 tff(4916,plain,
% 1.54/1.80 (b(elem!1, z) <=> b(s(z), z)),
% 1.54/1.80 inference(symmetry,[status(thm)],[4915])).
% 1.54/1.80 tff(4917,plain,
% 1.54/1.80 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4916])).
% 1.64/1.80 tff(4918,plain,
% 1.64/1.80 (~b(s(z), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4858, 4917])).
% 1.64/1.80 tff(4919,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4910, 4918])).
% 1.64/1.80 tff(4920,plain,((~b(z, s(z))) | b(elem!1, z) | b(s(z), elem!1) | (~r(s(s(s(s(z)))), elem!1)) | r(s(elem!1), elem!1) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4921,plain,
% 1.64/1.80 (b(elem!1, z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4920, 4822, 3062, 1301, 4381, 4854, 4821, 4370, 4771])).
% 1.64/1.80 tff(4922,plain,
% 1.64/1.80 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4923,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4922])).
% 1.64/1.80 tff(4924,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4923, 2064])).
% 1.64/1.80 tff(4925,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4926,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4925, 4924])).
% 1.64/1.80 tff(4927,plain,
% 1.64/1.80 (~b(s(s(s(z))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4926, 337, 4772, 4921, 4857])).
% 1.64/1.80 tff(4928,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4927, 4853])).
% 1.64/1.80 tff(4929,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(z), elem!1)) | r(s(elem!1), elem!1) | (~b(z, s(z))) | b(s(z), elem!1) | b(elem!1, s(z)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4930,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4929, 83, 4407, 3062, 4716, 4381, 4370, 4593, 4592, 4406, 4586, 1219])).
% 1.64/1.80 tff(4931,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[851, 4930])).
% 1.64/1.80 tff(4932,plain,
% 1.64/1.80 (~(s(s(s(z))) = elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1472, 4586])).
% 1.64/1.80 tff(4933,plain,
% 1.64/1.80 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4932, 4644])).
% 1.64/1.80 tff(4934,plain,
% 1.64/1.80 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4730, 4931, 4406])).
% 1.64/1.80 tff(4935,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4172, 4934, 83])).
% 1.64/1.80 tff(4936,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[700, 4935, 4720])).
% 1.64/1.80 tff(4937,plain,
% 1.64/1.80 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4936, 4752])).
% 1.64/1.80 tff(4938,plain,
% 1.64/1.80 (~r(s(s(s(z))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3923, 189, 777, 118])).
% 1.64/1.80 tff(4939,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4938, 4658])).
% 1.64/1.80 tff(4940,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1820, 4939, 692])).
% 1.64/1.80 tff(4941,plain,
% 1.64/1.80 (b(s(s(s(z))), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4940, 4656])).
% 1.64/1.80 tff(4942,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.80 tff(4943,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3611, 189, 811, 118])).
% 1.64/1.80 tff(4944,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[548, 4943])).
% 1.64/1.80 tff(4945,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4249, 189, 811, 118])).
% 1.64/1.80 tff(4946,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[524, 4945])).
% 1.64/1.80 tff(4947,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4948,plain,
% 1.64/1.80 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4949,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4948])).
% 1.64/1.80 tff(4950,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4949, 4947])).
% 1.64/1.80 tff(4951,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4952,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4951, 4950])).
% 1.64/1.80 tff(4953,plain,
% 1.64/1.80 (~b(s(s(s(z))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4952, 337, 4946, 4944, 4942])).
% 1.64/1.80 tff(4954,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4953, 4941])).
% 1.64/1.80 tff(4955,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4956,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4955, 4937, 4933, 4931, 83, 4406])).
% 1.64/1.80 tff(4957,plain,
% 1.64/1.80 (b(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[48, 4956])).
% 1.64/1.80 tff(4958,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4959,plain,
% 1.64/1.80 (((~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))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4960,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4959])).
% 1.64/1.80 tff(4961,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4960, 4958])).
% 1.64/1.80 tff(4962,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4963,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4962, 4961])).
% 1.64/1.80 tff(4964,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4963, 189, 4406, 4931])).
% 1.64/1.80 tff(4965,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[857, 4964, 4719])).
% 1.64/1.80 tff(4966,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4764, 4965, 4593, 4936, 83])).
% 1.64/1.80 tff(4967,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[832, 43, 4586, 4966])).
% 1.64/1.80 tff(4968,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2966, 189, 1077, 4967])).
% 1.64/1.80 tff(4969,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[820, 43, 817, 4968])).
% 1.64/1.80 tff(4970,plain,
% 1.64/1.80 (~r(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4698, 189, 1077, 4967])).
% 1.64/1.80 tff(4971,plain,
% 1.64/1.80 (b(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1584, 43, 4970, 1562])).
% 1.64/1.80 tff(4972,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4973,plain,
% 1.64/1.80 (((~b(z, s(s(s(s(z)))))) | (~b(elem!1, 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(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4974,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, 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(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4973])).
% 1.64/1.80 tff(4975,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, 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(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4974, 4972])).
% 1.64/1.80 tff(4976,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, 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(z, elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4977,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 1.64/1.80 tff(4978,plain,
% 1.64/1.80 (~b(z, elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4977, 337, 4971, 4969, 4937])).
% 1.64/1.80 tff(4979,plain,
% 1.64/1.80 (r(z, elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[921, 4978, 4717])).
% 1.64/1.80 tff(4980,plain,
% 1.64/1.80 (~r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3855, 4979, 4407])).
% 1.64/1.80 tff(4981,plain,
% 1.64/1.80 (b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[963, 4980])).
% 1.64/1.80 tff(4982,plain,
% 1.64/1.80 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4586, 4629])).
% 1.64/1.80 tff(4983,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~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)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4984,plain,
% 1.64/1.80 (((~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~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)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4985,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4984])).
% 1.64/1.80 tff(4986,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~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)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4985, 4983])).
% 1.64/1.80 tff(4987,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4988,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~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))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 1.64/1.80 tff(4989,plain,
% 1.64/1.80 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4988, 337, 4593, 4965, 4937])).
% 1.64/1.80 tff(4990,plain,
% 1.64/1.80 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4640, 43, 4989])).
% 1.64/1.80 tff(4991,plain,
% 1.64/1.80 (r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4990, 4982])).
% 1.64/1.80 tff(4992,plain,
% 1.64/1.80 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4191, 337, 4981, 4716, 4969])).
% 1.64/1.80 tff(4993,plain,
% 1.64/1.80 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1150, 4992])).
% 1.64/1.80 tff(4994,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4995,plain,
% 1.64/1.80 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4996,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4995])).
% 1.64/1.80 tff(4997,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4996, 4994])).
% 1.64/1.80 tff(4998,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4999,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 1.64/1.81 tff(5000,plain,
% 1.64/1.81 (~r(s(elem!1), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4999, 189, 4993, 4991])).
% 1.64/1.81 tff(5001,plain,
% 1.64/1.81 (b(s(elem!1), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[898, 5000, 4718])).
% 1.64/1.81 tff(5002,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.64/1.81 tff(5003,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5004,plain,
% 1.64/1.81 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5005,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5004])).
% 1.64/1.81 tff(5006,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5005, 5003])).
% 1.64/1.81 tff(5007,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5008,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 1.64/1.81 tff(5009,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5008, 337, 1544, 1, 1301, 1658, 5002])).
% 1.64/1.81 tff(5010,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5011,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5010, 5001, 4981, 4716, 4957])).
% 1.64/1.81 tff(5012,plain,
% 1.64/1.81 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4678, 43, 4825, 5011])).
% 1.64/1.81 tff(5013,plain,
% 1.64/1.81 (~b(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4299, 4981, 4716, 4957])).
% 1.64/1.81 tff(5014,plain,
% 1.64/1.81 (r(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1498, 5013])).
% 1.64/1.81 tff(5015,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5016,plain,
% 1.64/1.81 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5017,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5016])).
% 1.64/1.81 tff(5018,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5017, 5015])).
% 1.64/1.81 tff(5019,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5020,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 1.64/1.81 tff(5021,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5020, 189, 1077, 5014, 5012])).
% 1.64/1.81 tff(5022,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(z, s(elem!1))) | r(s(elem!1), elem!1) | b(s(z), elem!1) | b(elem!1, s(z)) | (~r(s(elem!1), z)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5023,plain,
% 1.64/1.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5022, 4384, 3062, 4381, 4370, 1077, 282, 4585, 247])).
% 1.64/1.81 tff(5024,plain,
% 1.64/1.81 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[427, 5023])).
% 1.64/1.81 tff(5025,plain,
% 1.64/1.81 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[579, 5024, 4385])).
% 1.64/1.81 tff(5026,plain,
% 1.64/1.81 (~(s(elem!1) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[264, 5023])).
% 1.64/1.81 tff(5027,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[270, 5026, 3062])).
% 1.64/1.81 tff(5028,plain,
% 1.64/1.81 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[363, 5023, 4425])).
% 1.64/1.81 tff(5029,plain,
% 1.64/1.81 (r(elem!1, s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3157, 5028, 3062, 4585, 5026])).
% 1.64/1.81 tff(5030,plain,
% 1.64/1.81 (~r(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1032, 5029, 1077])).
% 1.64/1.81 tff(5031,plain,
% 1.64/1.81 (b(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1759, 5030, 4405])).
% 1.64/1.81 tff(5032,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5033,plain,
% 1.64/1.81 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5034,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5033])).
% 1.64/1.81 tff(5035,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5034, 5032])).
% 1.64/1.81 tff(5036,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5037,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 1.64/1.81 tff(5038,plain,
% 1.64/1.81 (~r(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5037, 189, 1077, 5029])).
% 1.64/1.81 tff(5039,plain,
% 1.64/1.81 (b(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[921, 5038, 4717])).
% 1.64/1.81 tff(5040,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5041,plain,
% 1.64/1.81 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(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, z)) | (~b(z, elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5042,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5041])).
% 1.64/1.81 tff(5043,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5042, 5040])).
% 1.64/1.81 tff(5044,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5045,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 1.64/1.81 tff(5046,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5045, 337, 5039, 5031, 4585, 5027, 5025])).
% 1.64/1.81 tff(5047,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | r(s(elem!1), elem!1) | b(s(z), elem!1) | b(elem!1, s(z)) | (elem!1 = s(z)) | b(s(elem!1), z) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5048,plain,
% 1.64/1.81 (b(s(elem!1), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5047, 4383, 247, 3062, 4370, 147, 1077, 4381])).
% 1.64/1.81 tff(5049,plain,
% 1.64/1.81 (~(s(elem!1) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2886, 2883, 1077])).
% 1.64/1.81 tff(5050,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[270, 5049, 3062])).
% 1.64/1.81 tff(5051,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3968, 337, 4382, 1763, 5050, 5048])).
% 1.64/1.81 tff(5052,plain,(r(z, elem!1) | (~b(elem!1, z)) | (elem!1 = s(z)) | r(s(elem!1), elem!1) | b(elem!1, s(z)) | (~r(z, s(elem!1))) | b(s(z), elem!1) | b(z, s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5053,plain,
% 1.64/1.81 (r(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5052, 1763, 3850, 3062, 4370, 148, 4380, 82, 65])).
% 1.64/1.81 tff(5054,plain,
% 1.64/1.81 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4748, 5053, 1, 4371, 1301])).
% 1.64/1.81 tff(5055,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4172, 5054, 83])).
% 1.64/1.81 tff(5056,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[700, 5055, 4091])).
% 1.64/1.81 tff(5057,plain,
% 1.64/1.81 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5056, 4086])).
% 1.64/1.81 tff(5058,plain,
% 1.64/1.81 (r(s(z), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[727, 4380, 136])).
% 1.64/1.81 tff(5059,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4119, 5053, 5058])).
% 1.64/1.81 tff(5060,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[857, 5059, 853])).
% 1.64/1.81 tff(5061,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5062,plain,
% 1.64/1.81 (((~b(s(s(s(s(z)))), elem!1)) | (~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(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5063,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5062])).
% 1.64/1.81 tff(5064,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5063, 5061])).
% 1.64/1.81 tff(5065,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5066,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5065, 5064])).
% 1.64/1.81 tff(5067,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5066, 337, 5060, 5057, 4373])).
% 1.64/1.81 tff(5068,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[548, 5067])).
% 1.64/1.81 tff(5069,plain,
% 1.64/1.81 ((~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4955, 116])).
% 1.64/1.81 tff(5070,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5069, 5057, 83, 4371, 118])).
% 1.64/1.81 tff(5071,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[851, 5070])).
% 1.64/1.81 tff(5072,plain,
% 1.64/1.81 (~b(z, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4738, 337, 1, 1301, 5071])).
% 1.64/1.81 tff(5073,plain,
% 1.64/1.81 (r(z, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1786, 5072])).
% 1.64/1.81 tff(5074,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1333, 189, 1339, 1115, 1474])).
% 1.64/1.81 tff(5075,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5076,plain,
% 1.64/1.81 (~r(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5075, 5073, 5068])).
% 1.64/1.81 tff(5077,plain,
% 1.64/1.81 (b(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1498, 5076])).
% 1.64/1.81 tff(5078,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5079,plain,
% 1.64/1.81 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5080,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5079])).
% 1.64/1.81 tff(5081,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5080, 5078])).
% 1.64/1.81 tff(5082,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5083,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5082, 5081])).
% 1.64/1.81 tff(5084,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5083, 337, 1763, 1, 1301, 5077, 4373])).
% 1.64/1.81 tff(5085,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | r(s(elem!1), elem!1) | b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5086,plain,
% 1.64/1.81 (~b(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5085, 4370, 1301, 83, 118, 853, 3062, 1, 82, 65])).
% 1.64/1.81 tff(5087,plain,
% 1.64/1.81 (r(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1759, 5086, 3768])).
% 1.64/1.81 tff(5088,plain,
% 1.64/1.81 (~r(elem!1, s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1032, 5087, 148])).
% 1.64/1.81 tff(5089,plain,
% 1.64/1.81 (~(elem!1 = s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[980, 5049])).
% 1.64/1.81 tff(5090,plain,
% 1.64/1.81 (b(elem!1, s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1015, 5089, 1010])).
% 1.64/1.81 tff(5091,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5092,plain,
% 1.64/1.81 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~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(elem!1, s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5093,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X1, 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(elem!1, s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5092])).
% 1.64/1.81 tff(5094,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X1, 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(elem!1, s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5093, 5091])).
% 1.64/1.81 tff(5095,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5096,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 1.64/1.81 tff(5097,plain,
% 1.64/1.81 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5096, 337, 4382, 5050, 5090, 5048])).
% 1.64/1.82 tff(5098,plain,(r(z, elem!1) | r(elem!1, s(elem!1)) | (elem!1 = s(z)) | r(s(elem!1), elem!1) | b(elem!1, s(z)) | (~r(z, s(elem!1))) | b(s(z), elem!1) | b(z, s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5099,plain,
% 1.64/1.82 (r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5098, 4381, 3850, 3062, 4370, 148, 5088, 82, 65])).
% 1.64/1.82 tff(5100,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4748, 5099, 1, 4371, 1301])).
% 1.64/1.82 tff(5101,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4172, 5100, 83])).
% 1.64/1.82 tff(5102,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[700, 5101, 4091])).
% 1.64/1.82 tff(5103,plain,
% 1.64/1.82 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5102, 4086])).
% 1.64/1.82 tff(5104,plain,
% 1.64/1.82 (r(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[727, 4381, 136])).
% 1.64/1.82 tff(5105,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4119, 5099, 5104])).
% 1.64/1.82 tff(5106,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[857, 5105, 853])).
% 1.64/1.82 tff(5107,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5066, 337, 5106, 5103, 4373])).
% 1.64/1.82 tff(5108,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[548, 5107])).
% 1.64/1.82 tff(5109,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5069, 5103, 83, 4371, 118])).
% 1.64/1.82 tff(5110,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[851, 5109])).
% 1.64/1.82 tff(5111,plain,
% 1.64/1.82 (~b(z, s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4738, 337, 1, 1301, 5110])).
% 1.64/1.82 tff(5112,plain,
% 1.64/1.82 (r(z, s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1786, 5111])).
% 1.64/1.82 tff(5113,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5114,plain,
% 1.64/1.82 (((~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(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5115,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5114])).
% 1.64/1.82 tff(5116,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5115, 5113])).
% 1.64/1.82 tff(5117,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5118,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5117, 5116])).
% 1.64/1.82 tff(5119,plain,
% 1.64/1.82 (~r(z, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5118, 189, 1339, 1115])).
% 1.64/1.82 tff(5120,plain,
% 1.64/1.82 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[199, 43, 5119])).
% 1.64/1.82 tff(5121,plain,
% 1.64/1.82 (b(z, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5120, 179])).
% 1.64/1.82 tff(5122,plain,
% 1.64/1.82 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3590, 189, 1339, 4222])).
% 1.64/1.82 tff(5123,plain,
% 1.64/1.82 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4268, 5122])).
% 1.64/1.82 tff(5124,plain,
% 1.64/1.82 (~r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5075, 1115, 1339])).
% 1.64/1.82 tff(5125,plain,
% 1.64/1.82 (b(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1498, 5124])).
% 1.64/1.82 tff(5126,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5127,plain,
% 1.64/1.82 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5128,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5127])).
% 1.64/1.82 tff(5129,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5128, 5126])).
% 1.64/1.82 tff(5130,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5131,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5130, 5129])).
% 1.64/1.82 tff(5132,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5131, 337, 1301, 4340, 5125, 5123, 5121])).
% 1.64/1.82 tff(5133,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(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5134,plain,
% 1.64/1.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5133, 5112, 1301, 5108])).
% 1.64/1.82 tff(5135,plain,
% 1.64/1.82 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2268, 5134])).
% 1.64/1.82 tff(5136,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2027, 5108, 118])).
% 1.64/1.82 tff(5137,plain,
% 1.64/1.82 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1150, 5136])).
% 1.64/1.82 tff(5138,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5139,plain,
% 1.64/1.82 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5140,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5139])).
% 1.64/1.82 tff(5141,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5140, 5138])).
% 1.64/1.82 tff(5142,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(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))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5143,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5142, 5141])).
% 1.64/1.82 tff(5144,plain,
% 1.64/1.82 (~b(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5143, 337, 5137, 5106, 5135, 5103])).
% 1.64/1.82 tff(5145,plain,
% 1.64/1.82 (r(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2229, 5144])).
% 1.64/1.82 tff(5146,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5147,plain,
% 1.64/1.82 (((~b(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5148,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5147])).
% 1.64/1.82 tff(5149,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5148, 5146])).
% 1.64/1.82 tff(5150,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5151,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5150, 5149])).
% 1.64/1.82 tff(5152,plain,
% 1.64/1.82 (~b(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5151, 337, 5106, 5135, 5103])).
% 1.64/1.82 tff(5153,plain,
% 1.64/1.82 (r(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2301, 5152, 4103])).
% 1.64/1.82 tff(5154,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5155,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5156,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5155, 5154])).
% 1.64/1.82 tff(5157,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5156, 189, 4371, 5153, 5145])).
% 1.64/1.82 tff(5158,plain,(b(s(z), elem!1) | (s(s(z)) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(s(z)))) = elem!1) | r(s(elem!1), elem!1) | b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5159,plain,
% 1.64/1.82 (b(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5158, 4370, 1301, 1, 118, 83, 853, 3062, 4103, 82, 65])).
% 1.64/1.82 tff(5160,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5161,plain,
% 1.64/1.82 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5162,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~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(X1, 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(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5161])).
% 1.64/1.82 tff(5163,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~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(X1, 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(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5162, 5160])).
% 1.64/1.82 tff(5164,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5165,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 1.64/1.82 tff(5166,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5165, 337, 4382, 5050, 791, 5090, 1301])).
% 1.64/1.82 tff(5167,plain,(r(z, elem!1) | (~b(s(z), elem!1)) | (~b(z, s(z))) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1) | (~r(z, s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5168,plain,
% 1.64/1.82 (r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5167, 5159, 1301, 5088, 3062, 148, 65])).
% 1.64/1.82 tff(5169,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4748, 5168, 1, 4371, 1301])).
% 1.64/1.82 tff(5170,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4172, 5169, 83])).
% 1.64/1.82 tff(5171,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[700, 5170, 4091])).
% 1.64/1.82 tff(5172,plain,
% 1.64/1.82 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5171, 4086])).
% 1.64/1.82 tff(5173,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5069, 5172, 83, 4371, 118])).
% 1.64/1.82 tff(5174,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[851, 5173])).
% 1.64/1.82 tff(5175,plain,
% 1.64/1.82 (~b(s(s(s(s(z)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4117, 337, 1, 1301, 5174])).
% 1.64/1.82 tff(5176,plain,
% 1.64/1.82 (r(s(s(s(s(z)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1792, 5175])).
% 1.64/1.82 tff(5177,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1177, 5176, 5087])).
% 1.64/1.82 tff(5178,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[857, 5177, 853])).
% 1.64/1.82 tff(5179,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3916, 189, 4371, 118])).
% 1.64/1.82 tff(5180,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5179, 3848])).
% 1.64/1.82 tff(5181,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3252, 5180])).
% 1.64/1.82 tff(5182,plain,
% 1.64/1.82 (b(elem!1, s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5181, 3846])).
% 1.64/1.82 tff(5183,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5184,plain,
% 1.64/1.82 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5185,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5184])).
% 1.64/1.82 tff(5186,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5185, 5183])).
% 1.64/1.82 tff(5187,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5188,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5187, 5186])).
% 1.64/1.82 tff(5189,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5188, 337, 5159, 5174, 5172, 4373, 5182])).
% 1.64/1.82 tff(5190,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[548, 5189])).
% 1.64/1.82 tff(5191,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2027, 5190, 118])).
% 1.64/1.82 tff(5192,plain,
% 1.64/1.82 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1150, 5191])).
% 1.64/1.82 tff(5193,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5194,plain,
% 1.64/1.83 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~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), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5195,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5194])).
% 1.64/1.83 tff(5196,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5195, 5193])).
% 1.64/1.83 tff(5197,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~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)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5198,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5197, 5196])).
% 1.64/1.83 tff(5199,plain,
% 1.64/1.83 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5198, 337, 5159, 5174, 5172])).
% 1.64/1.83 tff(5200,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5199, 5192, 5178])).
% 1.64/1.83 tff(5201,plain,(b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | r(s(elem!1), elem!1) | (z = elem!1) | (s(s(z)) = elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5202,plain,
% 1.64/1.83 (r(s(elem!1), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5201, 4369, 118, 4083, 3844, 83, 171, 61, 156, 82])).
% 1.64/1.83 tff(5203,plain,
% 1.64/1.83 (~r(z, elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1748, 5202, 148])).
% 1.64/1.83 tff(5204,plain,
% 1.64/1.83 (b(z, elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[921, 5203, 61])).
% 1.64/1.83 tff(5205,plain,
% 1.64/1.83 (r(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[322, 4369, 3850])).
% 1.64/1.83 tff(5206,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3859, 777, 274])).
% 1.64/1.83 tff(5207,plain,
% 1.64/1.83 (b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[963, 5206])).
% 1.64/1.83 tff(5208,plain,
% 1.64/1.83 (~r(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2417, 273, 777])).
% 1.64/1.83 tff(5209,plain,
% 1.64/1.83 (b(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[898, 5208, 50])).
% 1.64/1.83 tff(5210,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5211,plain,
% 1.64/1.83 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5212,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5211])).
% 1.64/1.83 tff(5213,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5212, 5210])).
% 1.64/1.83 tff(5214,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5215,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5214, 5213])).
% 1.64/1.83 tff(5216,plain,
% 1.64/1.83 (~b(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5215, 337, 925, 5209, 5207, 1301])).
% 1.64/1.83 tff(5217,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5218,plain,
% 1.64/1.83 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5219,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5218])).
% 1.64/1.83 tff(5220,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5219, 5217])).
% 1.64/1.83 tff(5221,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5222,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5221, 5220])).
% 1.64/1.83 tff(5223,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5222, 189, 274, 273, 1219])).
% 1.64/1.83 tff(5224,plain,((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5225,plain,
% 1.64/1.83 (~r(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5224, 273, 274])).
% 1.64/1.83 tff(5226,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[378, 43, 114, 5225, 5216])).
% 1.64/1.83 tff(5227,plain,((~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5228,plain,
% 1.64/1.83 (~r(elem!1, z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5227, 5204, 3844, 50, 5205, 5202])).
% 1.64/1.83 tff(5229,plain,
% 1.64/1.83 (b(elem!1, z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1759, 5228, 68])).
% 1.64/1.83 tff(5230,plain,
% 1.64/1.83 (~b(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4005, 5229, 3844, 5204])).
% 1.64/1.83 tff(5231,plain,
% 1.64/1.83 (r(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[727, 5230, 136])).
% 1.64/1.83 tff(5232,plain,
% 1.64/1.83 (~r(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4123, 5231, 118])).
% 1.64/1.83 tff(5233,plain,
% 1.64/1.83 (b(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2463, 5232, 117])).
% 1.64/1.83 tff(5234,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.83 tff(5235,plain,
% 1.64/1.83 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.83 inference(symmetry,[status(thm)],[5234])).
% 1.64/1.83 tff(5236,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5234])).
% 1.64/1.83 tff(5237,plain,
% 1.64/1.83 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[5236])).
% 1.64/1.83 tff(5238,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(elem!1), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5237, 5235])).
% 1.64/1.83 tff(5239,plain,
% 1.64/1.83 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5238])).
% 1.64/1.83 tff(5240,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[273, 5239])).
% 1.64/1.83 tff(5241,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5235])).
% 1.64/1.83 tff(5242,plain,
% 1.64/1.83 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5241])).
% 1.64/1.83 tff(5243,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[777, 5242])).
% 1.64/1.83 tff(5244,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(elem!1), s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5237])).
% 1.64/1.83 tff(5245,plain,
% 1.64/1.83 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5244])).
% 1.64/1.83 tff(5246,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[788, 5245])).
% 1.64/1.83 tff(5247,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5248,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5249,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 1.64/1.83 tff(5250,plain,
% 1.64/1.83 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5249, 189])).
% 1.64/1.83 tff(5251,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5250, 5246, 5243, 5240])).
% 1.64/1.83 tff(5252,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5253,plain,
% 1.64/1.83 (~r(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5252, 5202, 93, 5205])).
% 1.64/1.83 tff(5254,plain,
% 1.64/1.83 (b(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[898, 5253, 50])).
% 1.64/1.83 tff(5255,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[832, 43, 829, 1534])).
% 1.64/1.83 tff(5256,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[850, 4106, 846])).
% 1.64/1.83 tff(5257,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5258,plain,
% 1.64/1.83 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~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), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5259,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5258])).
% 1.64/1.83 tff(5260,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5259, 5257])).
% 1.64/1.83 tff(5261,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5262,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 1.64/1.83 tff(5263,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5262, 337, 1544, 1, 1301, 5256, 5255])).
% 1.64/1.83 tff(5264,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5265,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5264, 5231, 3844, 4083, 3970, 5202, 5254])).
% 1.64/1.83 tff(5266,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[857, 5265, 171])).
% 1.64/1.83 tff(5267,plain,
% 1.64/1.83 (~b(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2456, 5233, 5229, 5204])).
% 1.64/1.83 tff(5268,plain,
% 1.64/1.83 (r(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1498, 5267])).
% 1.64/1.83 tff(5269,plain,
% 1.64/1.83 (~b(z, s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2992, 5266, 5204, 5229])).
% 1.64/1.83 tff(5270,plain,
% 1.64/1.83 (r(z, s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1786, 5269])).
% 1.64/1.83 tff(5271,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5075, 5270, 5268])).
% 1.64/1.83 tff(5272,plain,
% 1.64/1.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[548, 5271])).
% 1.64/1.83 tff(5273,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5274,plain,
% 1.64/1.83 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5275,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5274])).
% 1.64/1.83 tff(5276,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5275, 5273])).
% 1.64/1.83 tff(5277,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5278,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5277, 5276])).
% 1.64/1.83 tff(5279,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5278, 337, 5204, 5229, 5272, 5266, 5233])).
% 1.64/1.83 tff(5280,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5281,plain,
% 1.64/1.84 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5280, 82, 50, 49])).
% 1.64/1.84 tff(5282,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.64/1.84 tff(5283,plain,
% 1.64/1.84 (b(z, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3843, 82, 50, 49])).
% 1.64/1.84 tff(5284,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1759, 4858, 68])).
% 1.64/1.84 tff(5285,plain,
% 1.64/1.84 (~r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5224, 273, 5284])).
% 1.64/1.84 tff(5286,plain,
% 1.64/1.84 (b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[378, 43, 114, 5285])).
% 1.64/1.84 tff(5287,plain,
% 1.64/1.84 (~r(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1699, 273, 82, 172, 50, 5284])).
% 1.64/1.84 tff(5288,plain,
% 1.64/1.84 (b(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[963, 5287])).
% 1.64/1.84 tff(5289,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5290,plain,
% 1.64/1.84 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5291,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5290])).
% 1.64/1.84 tff(5292,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5291, 5289])).
% 1.64/1.84 tff(5293,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5294,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 1.64/1.84 tff(5295,plain,
% 1.64/1.84 (~b(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5294, 337, 5288, 5283, 5286])).
% 1.64/1.84 tff(5296,plain,
% 1.64/1.84 (r(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2133, 43, 5295, 55])).
% 1.64/1.84 tff(5297,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1759, 4858, 3768])).
% 1.64/1.84 tff(5298,plain,
% 1.64/1.84 (~r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5224, 273, 5297])).
% 1.64/1.84 tff(5299,plain,
% 1.64/1.84 (b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[378, 43, 114, 5298])).
% 1.64/1.84 tff(5300,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5301,plain,
% 1.64/1.84 (((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(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(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5302,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5301])).
% 1.64/1.84 tff(5303,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5302, 5300])).
% 1.64/1.84 tff(5304,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(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)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5305,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 1.64/1.84 tff(5306,plain,
% 1.64/1.84 (~b(z, s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5305, 337, 600, 5299, 4755])).
% 1.64/1.84 tff(5307,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[839, 337, 600, 5299, 4755])).
% 1.64/1.84 tff(5308,plain,
% 1.64/1.84 (~(s(elem!1) = s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3076, 65])).
% 1.64/1.84 tff(5309,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1759, 3768, 4858])).
% 1.64/1.84 tff(5310,plain,
% 1.64/1.84 (~r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5224, 5309, 273])).
% 1.64/1.84 tff(5311,plain,
% 1.64/1.84 (b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[378, 43, 114, 5310])).
% 1.64/1.84 tff(5312,plain,
% 1.64/1.84 (~r(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1699, 5309, 82, 273, 5308, 172])).
% 1.64/1.84 tff(5313,plain,
% 1.64/1.84 (b(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[963, 5312])).
% 1.64/1.84 tff(5314,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5315,plain,
% 1.64/1.84 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5316,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5315])).
% 1.64/1.84 tff(5317,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5316, 5314])).
% 1.64/1.84 tff(5318,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5319,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 1.64/1.84 tff(5320,plain,
% 1.64/1.84 (~b(s(elem!1), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5319, 337, 5313, 1301, 5311])).
% 1.64/1.84 tff(5321,plain,
% 1.64/1.84 (r(s(elem!1), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[898, 5320, 5308])).
% 1.64/1.84 tff(5322,plain,
% 1.64/1.84 (~(s(z) = s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5308, 4011])).
% 1.64/1.84 tff(5323,plain,
% 1.64/1.84 (~b(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5294, 337, 5313, 1301, 5311])).
% 1.64/1.84 tff(5324,plain,
% 1.64/1.84 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2133, 43, 5323])).
% 1.64/1.84 tff(5325,plain,
% 1.64/1.84 (r(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5324, 5322])).
% 1.64/1.84 tff(5326,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.64/1.84 tff(5327,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1177, 274, 1168])).
% 1.64/1.84 tff(5328,plain,
% 1.64/1.84 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[809, 5327, 273])).
% 1.64/1.84 tff(5329,plain,
% 1.64/1.84 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5328, 4629])).
% 1.64/1.84 tff(5330,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5331,plain,
% 1.64/1.84 (((~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(elem!1, s(s(s(s(z)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5332,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5331])).
% 1.64/1.84 tff(5333,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5332, 5330])).
% 1.64/1.84 tff(5334,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5335,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5334, 5333])).
% 1.64/1.84 tff(5336,plain,
% 1.64/1.84 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5335, 189, 274, 1168])).
% 1.64/1.84 tff(5337,plain,
% 1.64/1.84 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2760, 802])).
% 1.64/1.84 tff(5338,plain,
% 1.64/1.84 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2845, 43, 5337, 5336])).
% 1.64/1.84 tff(5339,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[857, 802, 5327])).
% 1.64/1.84 tff(5340,plain,
% 1.64/1.84 (~r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2099, 788, 273])).
% 1.64/1.84 tff(5341,plain,
% 1.64/1.84 (b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[727, 5340, 272])).
% 1.64/1.84 tff(5342,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5343,plain,
% 1.64/1.84 (((~b(s(s(s(s(z)))), elem!1)) | (~b(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(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5344,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5343])).
% 1.64/1.84 tff(5345,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5344, 5342])).
% 1.64/1.84 tff(5346,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5347,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 1.64/1.84 tff(5348,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5347, 337, 5341, 5339, 5338])).
% 1.64/1.84 tff(5349,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[851, 5348])).
% 1.64/1.84 tff(5350,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(s(z)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5351,plain,
% 1.64/1.84 (((~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(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5352,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(s(z))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5351])).
% 1.64/1.84 tff(5353,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(s(z)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5352, 5350])).
% 1.64/1.84 tff(5354,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5355,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(s(z))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5354, 5353])).
% 1.64/1.84 tff(5356,plain,
% 1.64/1.84 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5355, 189, 788, 5349])).
% 1.64/1.84 tff(5357,plain,
% 1.64/1.84 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4640, 43, 5356])).
% 1.64/1.84 tff(5358,plain,
% 1.64/1.84 (b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5357, 5329])).
% 1.64/1.84 tff(5359,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[827, 189, 788, 5349])).
% 1.64/1.84 tff(5360,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[832, 43, 5328, 5359])).
% 1.64/1.84 tff(5361,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5362,plain,
% 1.64/1.84 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5363,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5362])).
% 1.64/1.84 tff(5364,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5363, 5361])).
% 1.64/1.84 tff(5365,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5366,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5365, 5364])).
% 1.64/1.84 tff(5367,plain,
% 1.64/1.84 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5366, 337, 599, 5360, 5338])).
% 1.64/1.84 tff(5368,plain,
% 1.64/1.84 (~b(elem!1, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5367, 5358])).
% 1.64/1.84 tff(5369,plain,
% 1.64/1.84 (r(elem!1, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1015, 5368, 1008])).
% 1.64/1.84 tff(5370,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5371,plain,
% 1.64/1.84 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5372,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5371])).
% 1.64/1.84 tff(5373,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5372, 5370])).
% 1.64/1.84 tff(5374,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5375,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 1.64/1.84 tff(5376,plain,
% 1.64/1.84 (~r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5375, 189, 5369, 5326])).
% 1.64/1.85 tff(5377,plain,
% 1.64/1.85 (b(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[322, 5376, 247])).
% 1.64/1.85 tff(5378,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5379,plain,
% 1.64/1.85 (((~b(s(s(s(s(z)))), elem!1)) | (~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), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5380,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5379])).
% 1.64/1.85 tff(5381,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5380, 5378])).
% 1.64/1.85 tff(5382,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5383,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5382, 5381])).
% 1.64/1.85 tff(5384,plain,
% 1.64/1.85 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5383, 337, 5341, 5339, 5338])).
% 1.64/1.85 tff(5385,plain,
% 1.64/1.85 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1150, 5384])).
% 1.64/1.85 tff(5386,plain,
% 1.64/1.85 (~(s(s(s(z))) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1472, 5328])).
% 1.64/1.85 tff(5387,plain,
% 1.64/1.85 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1528])).
% 1.64/1.85 tff(5388,plain,
% 1.64/1.85 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5387])).
% 1.64/1.85 tff(5389,plain,
% 1.64/1.85 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5388])).
% 1.64/1.85 tff(5390,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[116, 5389])).
% 1.64/1.85 tff(5391,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(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(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5392,plain,
% 1.64/1.85 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5393,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5392])).
% 1.64/1.85 tff(5394,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5393, 5391])).
% 1.64/1.85 tff(5395,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5396,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5395, 5394])).
% 1.64/1.85 tff(5397,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5396, 337, 2, 1603, 4942, 4826])).
% 1.64/1.85 tff(5398,plain,
% 1.64/1.85 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 5397])).
% 1.64/1.85 tff(5399,plain,
% 1.64/1.85 (~b(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4133, 337, 327, 2, 1603, 4942])).
% 1.64/1.85 tff(5400,plain,
% 1.64/1.85 (r(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 5399])).
% 1.64/1.85 tff(5401,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2483, 189, 273, 5400, 5398])).
% 1.64/1.85 tff(5402,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = elem!1) | (~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(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5403,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5402, 5390, 273, 5386, 5339, 5338, 5358, 5377])).
% 1.64/1.85 tff(5404,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[548, 5403])).
% 1.64/1.85 tff(5405,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2027, 5404, 5385])).
% 1.64/1.85 tff(5406,plain,
% 1.64/1.85 (b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[48, 5405])).
% 1.64/1.85 tff(5407,plain,
% 1.64/1.85 (~b(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1667, 5406, 1301, 5341, 5377])).
% 1.64/1.85 tff(5408,plain,
% 1.64/1.85 (r(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1498, 5407])).
% 1.64/1.85 tff(5409,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1333, 189, 5404, 1115, 5408])).
% 1.64/1.85 tff(5410,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5411,plain,
% 1.64/1.85 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5410, 5325, 1301, 273, 247, 1115, 981, 5311, 5321, 5309, 3104])).
% 1.64/1.85 tff(5412,plain,
% 1.64/1.85 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[281, 5411])).
% 1.64/1.85 tff(5413,plain,
% 1.64/1.85 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[291, 5309, 147])).
% 1.64/1.85 tff(5414,plain,
% 1.64/1.85 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[295, 43, 5413])).
% 1.64/1.85 tff(5415,plain,
% 1.64/1.85 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5414, 5412])).
% 1.64/1.85 tff(5416,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1177, 5309, 3104])).
% 1.64/1.85 tff(5417,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[350, 766, 276])).
% 1.64/1.85 tff(5418,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5419,plain,
% 1.64/1.85 (((~b(s(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(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), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5420,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(s(s(elem!1))))) | (~b(s(z), elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5419])).
% 1.64/1.85 tff(5421,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5420, 5418])).
% 1.64/1.85 tff(5422,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5423,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))))) | (~b(s(z), elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5422, 5421])).
% 1.64/1.85 tff(5424,plain,
% 1.64/1.85 (~b(s(z), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5423, 337, 5417, 5341, 325])).
% 1.64/1.85 tff(5425,plain,
% 1.64/1.85 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[310, 43, 211, 5424])).
% 1.64/1.85 tff(5426,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5427,plain,
% 1.64/1.85 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5428,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5427])).
% 1.64/1.85 tff(5429,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5428, 5426])).
% 1.64/1.85 tff(5430,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5431,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5430, 5429])).
% 1.64/1.85 tff(5432,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5431, 189, 788, 1113, 298])).
% 1.64/1.85 tff(5433,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5434,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5433, 5425, 788])).
% 1.64/1.85 tff(5435,plain,
% 1.64/1.85 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[579, 5434, 428])).
% 1.64/1.85 tff(5436,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5437,plain,
% 1.64/1.85 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5438,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5437])).
% 1.64/1.85 tff(5439,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5438, 5436])).
% 1.64/1.85 tff(5440,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5441,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5440, 5439])).
% 1.64/1.85 tff(5442,plain,
% 1.64/1.85 (~b(elem!1, s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5441, 337, 5417, 5435, 325])).
% 1.64/1.85 tff(5443,plain,
% 1.64/1.85 (r(elem!1, s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1015, 5442, 981])).
% 1.64/1.85 tff(5444,plain,
% 1.64/1.85 (~r(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5375, 189, 5443, 5326])).
% 1.64/1.85 tff(5445,plain,
% 1.64/1.85 (b(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[322, 5444, 247])).
% 1.64/1.85 tff(5446,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5447,plain,
% 1.64/1.85 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5448,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5447])).
% 1.64/1.85 tff(5449,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5448, 5446])).
% 1.64/1.85 tff(5450,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5451,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5450, 5449])).
% 1.64/1.85 tff(5452,plain,
% 1.64/1.85 ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5451, 337, 327, 326, 791])).
% 1.64/1.85 tff(5453,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5452, 2454])).
% 1.64/1.85 tff(5454,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2473, 43, 2470, 5453])).
% 1.64/1.85 tff(5455,plain,
% 1.64/1.85 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1491, 337, 327, 791])).
% 1.64/1.85 tff(5456,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5455, 2454])).
% 1.64/1.85 tff(5457,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[48, 5456])).
% 1.64/1.85 tff(5458,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5459,plain,
% 1.64/1.85 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5460,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5459])).
% 1.64/1.85 tff(5461,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5460, 5458])).
% 1.64/1.85 tff(5462,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5463,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5462, 5461])).
% 1.64/1.86 tff(5464,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5463, 189, 298, 5457, 5454])).
% 1.64/1.86 tff(5465,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5466,plain,
% 1.64/1.86 (~b(s(s(s(z))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5465, 5425, 2451, 5445, 5341, 5417])).
% 1.64/1.86 tff(5467,plain,
% 1.64/1.86 (r(s(s(s(z))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1484, 43, 1590, 5466])).
% 1.64/1.86 tff(5468,plain,
% 1.64/1.86 (~r(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4209, 189, 370, 5467])).
% 1.64/1.86 tff(5469,plain,
% 1.64/1.86 (b(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1498, 5468])).
% 1.64/1.86 tff(5470,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5471,plain,
% 1.64/1.86 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5472,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5471])).
% 1.64/1.86 tff(5473,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5472, 5470])).
% 1.64/1.86 tff(5474,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5475,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5474, 5473])).
% 1.64/1.86 tff(5476,plain,
% 1.64/1.86 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5475, 337, 396, 5435, 599, 5469])).
% 1.64/1.86 tff(5477,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2483, 189, 273, 5467])).
% 1.64/1.86 tff(5478,plain,
% 1.64/1.86 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4678, 43, 5477])).
% 1.64/1.86 tff(5479,plain,
% 1.64/1.86 (s(s(s(z))) = s(elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5478, 5476])).
% 1.64/1.86 tff(5480,plain,
% 1.64/1.86 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5479])).
% 1.64/1.86 tff(5481,plain,
% 1.64/1.86 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.86 tff(5482,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5480, 5481])).
% 1.64/1.86 tff(5483,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5482])).
% 1.64/1.86 tff(5484,plain,
% 1.64/1.86 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5483])).
% 1.64/1.86 tff(5485,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.86 tff(5486,plain,
% 1.64/1.86 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(elem!1)), z))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5485])).
% 1.64/1.86 tff(5487,plain,
% 1.64/1.86 (~b(s(s(elem!1)), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1790, 5486])).
% 1.64/1.86 tff(5488,plain,
% 1.64/1.86 (r(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[467, 43, 209, 5487])).
% 1.64/1.86 tff(5489,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(s(s(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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5490,plain,
% 1.64/1.86 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5491,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5490])).
% 1.64/1.86 tff(5492,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5491, 5489])).
% 1.64/1.86 tff(5493,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5494,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5493, 5492])).
% 1.64/1.86 tff(5495,plain,
% 1.64/1.86 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5494, 337, 5417, 5341, 1301, 599])).
% 1.64/1.86 tff(5496,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5495, 5435])).
% 1.64/1.86 tff(5497,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[406, 43, 133, 5496])).
% 1.64/1.86 tff(5498,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5499,plain,
% 1.64/1.86 (((~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(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5500,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), z))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5499])).
% 1.64/1.86 tff(5501,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), z)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5500, 5498])).
% 1.64/1.86 tff(5502,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5503,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 1.64/1.86 tff(5504,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5503, 189, 5497, 5488])).
% 1.64/1.86 tff(5505,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5504, 5484])).
% 1.64/1.86 tff(5506,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(commutativity,[status(thm)],[])).
% 1.64/1.86 tff(5507,plain,
% 1.64/1.86 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5506])).
% 1.64/1.86 tff(5508,plain,
% 1.64/1.86 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5481])).
% 1.64/1.86 tff(5509,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5508])).
% 1.64/1.86 tff(5510,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5509, 5506])).
% 1.64/1.86 tff(5511,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5510, 5507])).
% 1.64/1.86 tff(5512,plain,
% 1.64/1.86 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5511])).
% 1.64/1.86 tff(5513,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2518, 5512])).
% 1.64/1.86 tff(5514,plain,
% 1.64/1.86 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5480])).
% 1.64/1.86 tff(5515,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5514, 5508])).
% 1.64/1.86 tff(5516,plain,
% 1.64/1.86 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5515])).
% 1.64/1.86 tff(5517,plain,
% 1.64/1.86 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5514])).
% 1.64/1.86 tff(5518,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[5517])).
% 1.64/1.86 tff(5519,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2510, 5479, 50])).
% 1.64/1.86 tff(5520,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[857, 5519, 803])).
% 1.64/1.86 tff(5521,plain,
% 1.64/1.86 (b(s(s(elem!1)), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5520, 5518])).
% 1.64/1.86 tff(5522,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~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(X1, 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5523,plain,
% 1.64/1.86 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5524,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X1, 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5523])).
% 1.64/1.86 tff(5525,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X1, 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5524, 5522])).
% 1.64/1.86 tff(5526,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5527,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5526, 5525])).
% 1.64/1.86 tff(5528,plain,
% 1.64/1.86 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5527, 337, 5445, 5417, 5341])).
% 1.64/1.86 tff(5529,plain,
% 1.64/1.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5528, 5521])).
% 1.64/1.86 tff(5530,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5529, 5516])).
% 1.64/1.86 tff(5531,plain,
% 1.64/1.86 (((~![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)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5532,plain,
% 1.64/1.86 ((~![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)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5533,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.64/1.86 tff(5534,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5533, 43])).
% 1.64/1.86 tff(5535,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5534, 5530, 5513])).
% 1.64/1.86 tff(5536,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5535, 5505])).
% 1.64/1.86 tff(5537,plain,((~r(z, elem!1)) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), elem!1) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5538,plain,
% 1.64/1.86 (~r(z, elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5537, 5416, 1790, 5308, 5311, 273, 247, 5325, 5415, 1301, 5321, 5411, 172])).
% 1.64/1.86 tff(5539,plain,
% 1.64/1.86 (b(z, elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[921, 5538, 65])).
% 1.64/1.86 tff(5540,plain,
% 1.64/1.86 (~r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2099, 5321, 273])).
% 1.64/1.86 tff(5541,plain,
% 1.64/1.86 (b(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[727, 5540, 272])).
% 1.64/1.86 tff(5542,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5543,plain,
% 1.64/1.86 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5544,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5543])).
% 1.64/1.86 tff(5545,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5544, 5542])).
% 1.64/1.86 tff(5546,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5547,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5546, 5545])).
% 1.64/1.86 tff(5548,plain,
% 1.64/1.86 ((~b(z, elem!1)) | (~b(elem!1, s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5547, 337, 5541, 1301, 5415])).
% 1.64/1.86 tff(5549,plain,
% 1.64/1.86 (~b(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5548, 5539])).
% 1.64/1.86 tff(5550,plain,
% 1.64/1.86 (r(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[322, 5549, 247])).
% 1.64/1.86 tff(5551,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2415, 189, 273, 5550, 5321])).
% 1.64/1.86 tff(5552,plain,((z = elem!1) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~b(z, s(z))) | b(s(s(s(s(z)))), z) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5553,plain,
% 1.64/1.87 (~r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5552, 5307, 65, 1301, 247, 172, 273, 82, 4858])).
% 1.64/1.87 tff(5554,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1786, 5553, 5306])).
% 1.64/1.87 tff(5555,plain,((~b(s(s(s(s(z)))), s(elem!1))) | (z = elem!1) | (~b(z, s(z))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | b(z, s(s(s(elem!1)))) | b(elem!1, z) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5556,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5555, 273, 5283, 247, 172, 61, 82, 4858, 600])).
% 1.64/1.87 tff(5557,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5558,plain,
% 1.64/1.87 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5559,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5558])).
% 1.64/1.87 tff(5560,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5559, 5557])).
% 1.64/1.87 tff(5561,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5562,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5561, 5560])).
% 1.64/1.87 tff(5563,plain,
% 1.64/1.87 (~b(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5562, 337, 600, 5288, 5286])).
% 1.64/1.87 tff(5564,plain,
% 1.64/1.87 (r(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[898, 5563, 50])).
% 1.64/1.87 tff(5565,plain,
% 1.64/1.87 (~r(elem!1, s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2417, 5564, 273])).
% 1.64/1.87 tff(5566,plain,
% 1.64/1.87 (b(elem!1, s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[322, 5565, 247])).
% 1.64/1.87 tff(5567,plain,
% 1.64/1.87 (s(s(s(z))) = elem!1),
% 1.64/1.87 inference(transitivity,[status(thm)],[162, 2735, 91])).
% 1.64/1.87 tff(5568,plain,
% 1.64/1.87 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5567])).
% 1.64/1.87 tff(5569,plain,
% 1.64/1.87 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5568])).
% 1.64/1.87 tff(5570,plain,
% 1.64/1.87 (b(s(s(s(z))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[327, 5569])).
% 1.64/1.87 tff(5571,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3, 5570])).
% 1.64/1.87 tff(5572,plain,((~(s(s(s(s(z)))) = s(elem!1))) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5573,plain,
% 1.64/1.87 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5572, 5566, 3])).
% 1.64/1.87 tff(5574,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[832, 43, 5573, 5556])).
% 1.64/1.87 tff(5575,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5576,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5577,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5576, 5575])).
% 1.64/1.87 tff(5578,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5577, 189, 5574, 5296])).
% 1.64/1.87 tff(5579,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[851, 5578])).
% 1.64/1.87 tff(5580,plain,
% 1.64/1.87 (~r(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2099, 5564, 273])).
% 1.64/1.87 tff(5581,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[727, 5580, 272])).
% 1.64/1.87 tff(5582,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5583,plain,
% 1.64/1.87 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5584,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), 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(X1, 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5583])).
% 1.64/1.87 tff(5585,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), 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(X1, 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5584, 5582])).
% 1.64/1.87 tff(5586,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5587,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5586, 5585])).
% 1.64/1.87 tff(5588,plain,
% 1.64/1.87 (~b(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5587, 337, 5566, 5581, 5283, 5579])).
% 1.64/1.87 tff(5589,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5590,plain,
% 1.64/1.87 (((~b(elem!1, s(z))) | (~b(z, 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(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5591,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5590])).
% 1.64/1.87 tff(5592,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5591, 5589])).
% 1.64/1.87 tff(5593,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5594,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 1.64/1.87 tff(5595,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5594, 337, 5566, 5581, 5283, 5579])).
% 1.64/1.87 tff(5596,plain,
% 1.64/1.87 (~r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5552, 5595, 61, 5283, 247, 172, 273, 82, 4858])).
% 1.64/1.87 tff(5597,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1786, 5596, 5588])).
% 1.64/1.87 tff(5598,plain,((~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(elem!1, z) | (~b(z, s(elem!1))) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5599,plain,
% 1.64/1.87 (~r(s(elem!1), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5598, 600, 172, 82, 4858, 247, 3, 50])).
% 1.64/1.87 tff(5600,plain,
% 1.64/1.87 (b(s(elem!1), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[270, 5599, 265])).
% 1.64/1.87 tff(5601,plain,
% 1.64/1.87 (b(elem!1, s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[322, 1075, 247])).
% 1.64/1.87 tff(5602,plain,
% 1.64/1.87 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5572, 5601, 3])).
% 1.64/1.87 tff(5603,plain,
% 1.64/1.87 (~b(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2594, 1878, 2520, 247, 1075])).
% 1.64/1.87 tff(5604,plain,
% 1.64/1.87 (r(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[898, 5603, 50])).
% 1.64/1.87 tff(5605,plain,
% 1.64/1.87 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5355, 189, 788, 811])).
% 1.64/1.87 tff(5606,plain,
% 1.64/1.87 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4640, 43, 5605])).
% 1.64/1.87 tff(5607,plain,
% 1.64/1.87 (b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5606, 4630])).
% 1.64/1.87 tff(5608,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5609,plain,
% 1.64/1.87 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5610,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5609])).
% 1.64/1.87 tff(5611,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5610, 5608])).
% 1.64/1.87 tff(5612,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5613,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5612, 5611])).
% 1.64/1.87 tff(5614,plain,
% 1.64/1.87 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5613, 337, 2520, 4944, 833])).
% 1.64/1.87 tff(5615,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5614, 5607])).
% 1.64/1.87 tff(5616,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4845, 189, 788, 118])).
% 1.64/1.87 tff(5617,plain,
% 1.64/1.87 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4678, 43, 5616])).
% 1.64/1.87 tff(5618,plain,
% 1.64/1.87 (s(s(s(z))) = s(elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5617, 5615])).
% 1.64/1.87 tff(5619,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5620,plain,
% 1.64/1.87 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~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), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5621,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5620])).
% 1.64/1.87 tff(5622,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5621, 5619])).
% 1.64/1.87 tff(5623,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5624,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5623, 5622])).
% 1.64/1.87 tff(5625,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5624, 337, 327, 600, 2520, 1301, 833])).
% 1.64/1.87 tff(5626,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1792, 5625])).
% 1.64/1.87 tff(5627,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1177, 5626, 274])).
% 1.64/1.87 tff(5628,plain,
% 1.64/1.87 (s(s(s(s(z)))) = elem!1),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[857, 5627, 229])).
% 1.64/1.87 tff(5629,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2510, 5628, 5618, 50])).
% 1.64/1.87 tff(5630,plain,((~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5631,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5630, 5604, 229, 274, 2520, 5601, 600, 1301, 829, 118, 50])).
% 1.64/1.87 tff(5632,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[851, 5631])).
% 1.64/1.87 tff(5633,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[727, 1878, 272])).
% 1.64/1.87 tff(5634,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5594, 337, 5601, 5633, 1301, 5632])).
% 1.64/1.87 tff(5635,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1792, 5634])).
% 1.64/1.87 tff(5636,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1177, 5635, 274])).
% 1.64/1.87 tff(5637,plain,
% 1.64/1.87 (s(s(s(s(z)))) = elem!1),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[857, 5636, 229])).
% 1.64/1.87 tff(5638,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[157])).
% 1.64/1.87 tff(5639,plain,
% 1.64/1.87 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5638])).
% 1.64/1.87 tff(5640,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[791, 5639])).
% 1.64/1.87 tff(5641,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.87 tff(5642,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5641, 5640])).
% 1.64/1.87 tff(5643,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,[]))).
% 1.64/1.87 tff(5644,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5643, 5637, 5633])).
% 1.64/1.87 tff(5645,plain,
% 1.64/1.87 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5637])).
% 1.64/1.88 tff(5646,plain,
% 1.64/1.88 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5645])).
% 1.64/1.88 tff(5647,plain,
% 1.64/1.88 (b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2520, 5646])).
% 1.64/1.88 tff(5648,plain,
% 1.64/1.88 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2510, 5637, 50])).
% 1.64/1.88 tff(5649,plain,
% 1.64/1.88 (~b(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5587, 337, 5601, 5633, 1301, 5632])).
% 1.64/1.88 tff(5650,plain,
% 1.64/1.88 (r(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1786, 5649])).
% 1.64/1.88 tff(5651,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4845, 189, 5604, 118])).
% 1.64/1.88 tff(5652,plain,
% 1.64/1.88 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4678, 43, 5651])).
% 1.64/1.88 tff(5653,plain,
% 1.64/1.88 (b(s(s(s(z))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5652, 5648])).
% 1.64/1.88 tff(5654,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5655,plain,
% 1.64/1.88 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5656,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5655])).
% 1.64/1.88 tff(5657,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5656, 5654])).
% 1.64/1.88 tff(5658,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5659,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 1.64/1.88 tff(5660,plain,
% 1.64/1.88 (~b(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5659, 337, 5601, 600, 2520, 1301, 5653])).
% 1.64/1.88 tff(5661,plain,
% 1.64/1.88 (r(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1498, 5660])).
% 1.64/1.88 tff(5662,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5075, 5661, 5650])).
% 1.64/1.88 tff(5663,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[548, 5662])).
% 1.64/1.88 tff(5664,plain,
% 1.64/1.88 (~r(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1493, 5661, 4645, 5633, 274, 5601])).
% 1.64/1.88 tff(5665,plain,
% 1.64/1.88 (b(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[963, 5664])).
% 1.64/1.88 tff(5666,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4847, 5665, 5663, 5604, 5648, 5647, 5644, 5632])).
% 1.64/1.88 tff(5667,plain,(r(s(z), elem!1) | (~r(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5668,plain,
% 1.64/1.88 (r(s(z), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5667, 5602, 600, 5600, 5283, 50, 229, 5284, 49, 247, 1075])).
% 1.64/1.88 tff(5669,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4119, 5668, 370])).
% 1.64/1.88 tff(5670,plain,
% 1.64/1.88 (s(s(s(s(z)))) = elem!1),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[857, 5669, 229])).
% 1.64/1.88 tff(5671,plain,
% 1.64/1.88 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5670])).
% 1.64/1.88 tff(5672,plain,
% 1.64/1.88 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5671])).
% 1.64/1.88 tff(5673,plain,
% 1.64/1.88 (r(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[370, 5672])).
% 1.64/1.88 tff(5674,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5670])).
% 1.64/1.88 tff(5675,plain,
% 1.64/1.88 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.88 inference(symmetry,[status(thm)],[5674])).
% 1.64/1.88 tff(5676,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), z)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5284, 5675])).
% 1.64/1.88 tff(5677,plain,
% 1.64/1.88 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[801, 5670, 247])).
% 1.64/1.88 tff(5678,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[281, 5677])).
% 1.64/1.88 tff(5679,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[291, 5284, 147])).
% 1.64/1.88 tff(5680,plain,
% 1.64/1.88 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[295, 43, 5679])).
% 1.64/1.88 tff(5681,plain,
% 1.64/1.88 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5680, 5678])).
% 1.64/1.88 tff(5682,plain,
% 1.64/1.88 (~r(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2896, 5668, 5284])).
% 1.64/1.88 tff(5683,plain,
% 1.64/1.88 (b(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[963, 5682])).
% 1.64/1.88 tff(5684,plain,
% 1.64/1.88 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2153, 985, 777])).
% 1.64/1.88 tff(5685,plain,
% 1.64/1.88 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[227, 43, 5684])).
% 1.64/1.88 tff(5686,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5685, 369])).
% 1.64/1.88 tff(5687,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[291, 274, 215])).
% 1.64/1.88 tff(5688,plain,
% 1.64/1.88 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[295, 43, 5687])).
% 1.64/1.88 tff(5689,plain,
% 1.64/1.88 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5688, 282])).
% 1.64/1.88 tff(5690,plain,
% 1.64/1.88 (~r(z, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2530, 5689, 172, 2520, 981, 274, 215])).
% 1.64/1.88 tff(5691,plain,
% 1.64/1.88 (b(z, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[395, 5690])).
% 1.64/1.88 tff(5692,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5693,plain,
% 1.64/1.88 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5694,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5693])).
% 1.64/1.88 tff(5695,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5694, 5692])).
% 1.64/1.88 tff(5696,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5697,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5696, 5695])).
% 1.64/1.88 tff(5698,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5697, 337, 5691, 1, 1301, 5686])).
% 1.64/1.88 tff(5699,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[406, 43, 133, 5698])).
% 1.64/1.88 tff(5700,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1048, 189, 274, 5699, 985])).
% 1.64/1.88 tff(5701,plain,((s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5702,plain,
% 1.64/1.88 (~r(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5701, 276, 274, 1301, 172, 2520, 215, 1, 984])).
% 1.64/1.88 tff(5703,plain,
% 1.64/1.88 (b(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[322, 5702, 247])).
% 1.64/1.88 tff(5704,plain,
% 1.64/1.88 (~b(z, elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[970, 337, 5703, 1, 1301])).
% 1.64/1.88 tff(5705,plain,
% 1.64/1.88 (r(z, elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[921, 5704, 65])).
% 1.64/1.88 tff(5706,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[752, 189, 5705, 985, 215])).
% 1.64/1.88 tff(5707,plain,((s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (z = elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5708,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5707, 5677, 147, 5283, 61, 5683, 5284, 247, 5600, 172])).
% 1.64/1.88 tff(5709,plain,
% 1.64/1.88 (~b(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[345, 5708, 5601, 5681])).
% 1.64/1.88 tff(5710,plain,
% 1.64/1.88 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1970, 5709])).
% 1.64/1.88 tff(5711,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5670])).
% 1.64/1.88 tff(5712,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2060, 5670, 5668, 49])).
% 1.64/1.88 tff(5713,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[548, 5712])).
% 1.64/1.88 tff(5714,plain,
% 1.64/1.88 (b(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5713, 5711])).
% 1.64/1.88 tff(5715,plain,
% 1.64/1.88 (~b(s(z), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5465, 5714, 2451, 5601, 5708, 5710])).
% 1.64/1.88 tff(5716,plain,
% 1.64/1.88 (r(s(z), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[727, 4381, 272])).
% 1.64/1.88 tff(5717,plain,
% 1.64/1.88 (r(elem!1, z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1759, 4405, 4858])).
% 1.64/1.88 tff(5718,plain,
% 1.64/1.88 (~r(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2896, 5717, 5716])).
% 1.64/1.88 tff(5719,plain,
% 1.64/1.88 (b(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[963, 5718])).
% 1.64/1.88 tff(5720,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1177, 5717, 1168])).
% 1.64/1.88 tff(5721,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5335, 189, 5717, 1168])).
% 1.64/1.88 tff(5722,plain,
% 1.64/1.88 (r(z, elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[921, 1516, 65])).
% 1.64/1.88 tff(5723,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[775])).
% 1.64/1.88 tff(5724,plain,
% 1.64/1.88 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5723])).
% 1.64/1.88 tff(5725,plain,
% 1.64/1.88 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2450, 5308])).
% 1.64/1.88 tff(5726,plain,
% 1.64/1.88 (~(s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 1.64/1.88 tff(5727,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[857, 802, 803])).
% 1.64/1.88 tff(5728,plain,
% 1.64/1.88 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1466, 775, 5308])).
% 1.64/1.88 tff(5729,plain,
% 1.64/1.88 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5728, 1845])).
% 1.64/1.88 tff(5730,plain,
% 1.64/1.88 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5729, 4629])).
% 1.64/1.88 tff(5731,plain,
% 1.64/1.88 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2845, 43, 4170])).
% 1.64/1.88 tff(5732,plain,
% 1.64/1.88 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5731, 5337])).
% 1.64/1.88 tff(5733,plain,
% 1.64/1.88 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4988, 337, 2520, 5727, 5732])).
% 1.64/1.88 tff(5734,plain,
% 1.64/1.88 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4640, 43, 5733])).
% 1.64/1.88 tff(5735,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5734, 5730])).
% 1.64/1.88 tff(5736,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5737,plain,
% 1.64/1.88 (((~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(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5738,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5737])).
% 1.64/1.88 tff(5739,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5738, 5736])).
% 1.64/1.88 tff(5740,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5741,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5740, 5739])).
% 1.64/1.88 tff(5742,plain,
% 1.64/1.88 (~r(s(elem!1), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5741, 189, 1115, 5735])).
% 1.64/1.88 tff(5743,plain,
% 1.64/1.88 (b(s(elem!1), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[378, 43, 114, 5742])).
% 1.64/1.88 tff(5744,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5745,plain,
% 1.64/1.88 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5746,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5745])).
% 1.64/1.88 tff(5747,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5746, 5744])).
% 1.64/1.88 tff(5748,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5749,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 1.64/1.88 tff(5750,plain,
% 1.64/1.88 (~r(z, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5749, 189, 1115, 5735])).
% 1.64/1.88 tff(5751,plain,
% 1.64/1.88 (b(z, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[395, 5750])).
% 1.64/1.88 tff(5752,plain,
% 1.64/1.88 (~b(s(elem!1), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5562, 337, 5751, 1, 5743])).
% 1.64/1.88 tff(5753,plain,
% 1.64/1.88 (r(s(elem!1), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[898, 5752, 5308])).
% 1.64/1.88 tff(5754,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5755,plain,
% 1.64/1.88 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5756,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5755])).
% 1.64/1.88 tff(5757,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5756, 5754])).
% 1.64/1.88 tff(5758,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5759,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 1.64/1.88 tff(5760,plain,
% 1.64/1.88 (~b(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5759, 337, 5751, 2520, 1, 5743])).
% 1.64/1.88 tff(5761,plain,
% 1.64/1.88 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2133, 43, 5760])).
% 1.64/1.88 tff(5762,plain,
% 1.64/1.88 (r(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5761, 5322])).
% 1.64/1.88 tff(5763,plain,
% 1.64/1.88 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4761, 337, 2520, 5727, 5732])).
% 1.64/1.88 tff(5764,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[832, 43, 5729, 5763])).
% 1.64/1.88 tff(5765,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5577, 189, 5764, 5762])).
% 1.64/1.88 tff(5766,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[851, 5765])).
% 1.64/1.88 tff(5767,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5768,plain,
% 1.64/1.88 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5769,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5768])).
% 1.64/1.88 tff(5770,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5769, 5767])).
% 1.64/1.88 tff(5771,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5772,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5771, 5770])).
% 1.64/1.88 tff(5773,plain,
% 1.64/1.88 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5772, 189, 5764, 5762])).
% 1.64/1.88 tff(5774,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1150, 5773])).
% 1.64/1.88 tff(5775,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5776,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(z)))))) | (~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(s(z), 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))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5777,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5776])).
% 1.64/1.88 tff(5778,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5777, 5775])).
% 1.64/1.88 tff(5779,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5780,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5779, 5778])).
% 1.64/1.88 tff(5781,plain,
% 1.64/1.88 (~b(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5780, 337, 5774, 5766, 5732])).
% 1.64/1.88 tff(5782,plain,
% 1.64/1.88 (r(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[322, 5781, 247])).
% 1.64/1.88 tff(5783,plain,
% 1.64/1.88 (~r(elem!1, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4434, 189, 5782, 5753])).
% 1.64/1.88 tff(5784,plain,
% 1.64/1.88 (b(elem!1, s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1015, 5783, 1008])).
% 1.64/1.88 tff(5785,plain,
% 1.64/1.89 (~r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4211, 1474, 370])).
% 1.64/1.89 tff(5786,plain,
% 1.64/1.89 (b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 5785])).
% 1.64/1.89 tff(5787,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3203, 189, 1474, 1168])).
% 1.64/1.89 tff(5788,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[548, 5787])).
% 1.64/1.89 tff(5789,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5790,plain,
% 1.64/1.89 (((~b(s(elem!1), 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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5791,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5790])).
% 1.64/1.89 tff(5792,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5791, 5789])).
% 1.64/1.89 tff(5793,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5794,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5793, 5792])).
% 1.64/1.89 tff(5795,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5794, 337, 2520, 982, 5788, 1603, 5786])).
% 1.64/1.89 tff(5796,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5797,plain,
% 1.64/1.89 (~r(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5796, 5784, 2520, 5727, 1168, 5726, 5722])).
% 1.64/1.89 tff(5798,plain,
% 1.64/1.89 (b(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1498, 5797])).
% 1.64/1.89 tff(5799,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5800,plain,
% 1.64/1.89 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5801,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5800])).
% 1.64/1.89 tff(5802,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5801, 5799])).
% 1.64/1.89 tff(5803,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5804,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 1.64/1.89 tff(5805,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5804, 337, 5751, 2520, 5743, 5798])).
% 1.64/1.89 tff(5806,plain,
% 1.64/1.89 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4678, 43, 5390, 5805])).
% 1.64/1.89 tff(5807,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4299, 5798, 1301, 1])).
% 1.64/1.89 tff(5808,plain,
% 1.64/1.89 (r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[48, 5807])).
% 1.64/1.89 tff(5809,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4845, 189, 5753, 5808, 5806])).
% 1.64/1.89 tff(5810,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(elem!1)) | (elem!1 = s(z)) | (~r(z, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z))))) | (z = elem!1) | r(s(s(s(s(z)))), elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5811,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5810, 5719, 1301, 2520, 1168, 981, 247, 1115, 5721, 4717, 5720, 82])).
% 1.64/1.89 tff(5812,plain,
% 1.64/1.89 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[281, 5811])).
% 1.64/1.89 tff(5813,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[291, 5717, 147])).
% 1.64/1.89 tff(5814,plain,
% 1.64/1.89 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[295, 43, 5813])).
% 1.64/1.89 tff(5815,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5814, 5812])).
% 1.64/1.89 tff(5816,plain,
% 1.64/1.89 (~r(z, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2530, 5815, 172, 2520, 981, 5717, 147])).
% 1.64/1.89 tff(5817,plain,
% 1.64/1.89 (b(z, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[395, 5816])).
% 1.64/1.89 tff(5818,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5707, 5811, 4717, 5719, 1301, 247, 5717, 172, 2520, 147])).
% 1.64/1.89 tff(5819,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5820,plain,
% 1.64/1.89 (((~b(s(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(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5821,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5820])).
% 1.64/1.89 tff(5822,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5821, 5819])).
% 1.64/1.89 tff(5823,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5824,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 1.64/1.89 tff(5825,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5824, 337, 5818, 2520, 5815])).
% 1.64/1.89 tff(5826,plain,
% 1.64/1.89 (r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[579, 5825, 428])).
% 1.64/1.89 tff(5827,plain,
% 1.64/1.89 (~r(s(elem!1), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1227, 5826, 147])).
% 1.64/1.89 tff(5828,plain,
% 1.64/1.89 (b(s(elem!1), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[378, 43, 114, 5827])).
% 1.64/1.89 tff(5829,plain,
% 1.64/1.89 (~b(s(elem!1), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5562, 337, 5817, 5719, 5828])).
% 1.64/1.89 tff(5830,plain,
% 1.64/1.89 (r(s(elem!1), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[898, 5829, 4718])).
% 1.64/1.89 tff(5831,plain,
% 1.64/1.89 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5433, 5830, 5826])).
% 1.64/1.89 tff(5832,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[310, 43, 211, 5831])).
% 1.64/1.89 tff(5833,plain,
% 1.64/1.89 (~b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[345, 5832, 5818, 5815])).
% 1.64/1.89 tff(5834,plain,
% 1.64/1.89 (r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[322, 5833, 247])).
% 1.64/1.89 tff(5835,plain,
% 1.64/1.89 (~r(elem!1, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4434, 189, 5834, 5830])).
% 1.64/1.89 tff(5836,plain,
% 1.64/1.89 (b(elem!1, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1015, 5835, 981])).
% 1.64/1.89 tff(5837,plain,
% 1.64/1.89 (~b(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2540, 5836, 2520, 5817])).
% 1.64/1.89 tff(5838,plain,
% 1.64/1.89 (r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[921, 5837, 4717])).
% 1.64/1.89 tff(5839,plain,
% 1.64/1.89 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2450, 4718])).
% 1.64/1.89 tff(5840,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5841,plain,
% 1.64/1.89 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5842,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5841])).
% 1.64/1.89 tff(5843,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.64/1.89 tff(5844,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5845,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.64/1.89 tff(5846,plain,
% 1.64/1.89 ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5845, 337, 5818, 5817, 2520, 5719])).
% 1.64/1.89 tff(5847,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5846, 5832])).
% 1.64/1.89 tff(5848,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[406, 43, 133, 5847])).
% 1.64/1.89 tff(5849,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5850,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5851,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5850, 5849])).
% 1.64/1.89 tff(5852,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5851, 189, 5848, 1168])).
% 1.64/1.89 tff(5853,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1947, 43, 2518, 5852])).
% 1.64/1.89 tff(5854,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5855,plain,
% 1.64/1.89 (((~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5856,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(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(X1, 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(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)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5855])).
% 1.64/1.89 tff(5857,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(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(X1, 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(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))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5856, 5854])).
% 1.64/1.89 tff(5858,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5859,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5858, 5857])).
% 1.64/1.89 tff(5860,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5859, 337, 5818, 5836, 5815, 5853])).
% 1.64/1.89 tff(5861,plain,
% 1.64/1.89 (s(s(s(s(z)))) = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[857, 5860, 5720])).
% 1.64/1.89 tff(5862,plain,
% 1.64/1.89 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2510, 5861, 4718])).
% 1.64/1.89 tff(5863,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5864,plain,
% 1.64/1.89 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5865,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5864])).
% 1.64/1.89 tff(5866,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5865, 5863])).
% 1.64/1.89 tff(5867,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5868,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5867, 5866])).
% 1.74/1.90 tff(5869,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5868, 337, 2520, 982, 2454])).
% 1.74/1.90 tff(5870,plain,
% 1.74/1.90 (r(s(s(s(z))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 5869])).
% 1.74/1.90 tff(5871,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5872,plain,
% 1.74/1.90 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5873,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5872])).
% 1.74/1.90 tff(5874,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5873, 5871])).
% 1.74/1.90 tff(5875,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5876,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5875, 5874])).
% 1.74/1.90 tff(5877,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5876, 337, 326, 2520, 982, 2454])).
% 1.74/1.90 tff(5878,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2473, 43, 2470, 5877])).
% 1.74/1.90 tff(5879,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5880,plain,
% 1.74/1.90 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5881,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5880])).
% 1.74/1.90 tff(5882,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5881, 5879])).
% 1.74/1.90 tff(5883,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5884,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5883, 5882])).
% 1.74/1.90 tff(5885,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5884, 189, 1113, 5878, 5870])).
% 1.74/1.90 tff(5886,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5887,plain,
% 1.74/1.90 (~b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5886, 5826, 5862, 5839, 2520, 5836, 5818])).
% 1.74/1.90 tff(5888,plain,
% 1.74/1.90 (elem!1 = s(s(s(s(z))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[5861])).
% 1.74/1.90 tff(5889,plain,
% 1.74/1.90 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5888])).
% 1.74/1.90 tff(5890,plain,
% 1.74/1.90 ((s(s(s(z))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5889, 504])).
% 1.74/1.90 tff(5891,plain,
% 1.74/1.90 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[5890])).
% 1.74/1.90 tff(5892,plain,
% 1.74/1.90 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5891])).
% 1.74/1.90 tff(5893,plain,
% 1.74/1.90 (~(s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[519, 5892])).
% 1.74/1.90 tff(5894,plain,
% 1.74/1.90 (r(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1484, 43, 5893, 5887])).
% 1.74/1.90 tff(5895,plain,
% 1.74/1.90 (~r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4211, 5894, 5838])).
% 1.74/1.90 tff(5896,plain,
% 1.74/1.90 (b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1498, 5895])).
% 1.74/1.90 tff(5897,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, 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(X1, 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(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5898,plain,
% 1.74/1.90 (((~b(elem!1, s(s(s(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)))), 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))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5899,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(elem!1))))) | (~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(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5898])).
% 1.74/1.90 tff(5900,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(elem!1))))) | (~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(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5899, 5897])).
% 1.74/1.90 tff(5901,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(elem!1))))) | (~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(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5902,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 1.74/1.90 tff(5903,plain,
% 1.74/1.90 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5902, 337, 5818, 5815, 5832, 5853])).
% 1.74/1.90 tff(5904,plain,
% 1.74/1.90 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1150, 5903])).
% 1.74/1.90 tff(5905,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5861])).
% 1.74/1.90 tff(5906,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[5905])).
% 1.74/1.90 tff(5907,plain,
% 1.74/1.90 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5906])).
% 1.74/1.90 tff(5908,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5887, 5907])).
% 1.74/1.90 tff(5909,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[548, 5908])).
% 1.74/1.90 tff(5910,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2027, 5909, 5904])).
% 1.74/1.90 tff(5911,plain,
% 1.74/1.90 (b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[48, 5910])).
% 1.74/1.90 tff(5912,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4299, 5911, 5896, 1301, 5719])).
% 1.74/1.90 tff(5913,plain,(b(s(z), elem!1) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | b(elem!1, z) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5914,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5913, 5715, 5676, 82, 247, 5600, 172, 5599, 5673, 4858, 5283])).
% 1.74/1.90 tff(5915,plain,(r(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, z) | (~r(z, elem!1)) | b(s(s(s(s(z)))), elem!1) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5916,plain,
% 1.74/1.90 (r(elem!1, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5915, 600, 247, 172, 4858, 370, 229, 82, 50, 3])).
% 1.74/1.90 tff(5917,plain,
% 1.74/1.90 (~r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3859, 5916, 5284])).
% 1.74/1.90 tff(5918,plain,
% 1.74/1.90 (b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[963, 5917])).
% 1.74/1.90 tff(5919,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4119, 5716, 370])).
% 1.74/1.90 tff(5920,plain,
% 1.74/1.90 (s(s(s(s(z)))) = elem!1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[857, 5919, 229])).
% 1.74/1.90 tff(5921,plain,
% 1.74/1.90 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5920])).
% 1.74/1.90 tff(5922,plain,
% 1.74/1.90 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[5921])).
% 1.74/1.90 tff(5923,plain,
% 1.74/1.90 (r(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[370, 5922])).
% 1.74/1.90 tff(5924,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5920])).
% 1.74/1.90 tff(5925,plain,
% 1.74/1.90 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(symmetry,[status(thm)],[5924])).
% 1.74/1.90 tff(5926,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[274, 5925])).
% 1.74/1.90 tff(5927,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5913, 5926, 5923, 82, 247, 3079, 172, 3062, 4381, 4858, 1301])).
% 1.74/1.90 tff(5928,plain,(b(s(z), elem!1) | b(z, s(s(s(elem!1)))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1) | b(elem!1, z) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5929,plain,
% 1.74/1.90 (b(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5928, 5599, 247, 172, 82, 4858, 5283, 5284, 370, 229])).
% 1.74/1.90 tff(5930,plain,
% 1.74/1.90 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(5931,plain,
% 1.74/1.90 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[5930])).
% 1.74/1.90 tff(5932,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[291, 5284, 215])).
% 1.74/1.90 tff(5933,plain,
% 1.74/1.90 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[295, 43, 5932])).
% 1.74/1.90 tff(5934,plain,
% 1.74/1.90 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5933, 282])).
% 1.74/1.90 tff(5935,plain,
% 1.74/1.90 (~(elem!1 = z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4863, 4370, 1301])).
% 1.74/1.90 tff(5936,plain,
% 1.74/1.90 (r(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1759, 5935, 4858])).
% 1.74/1.90 tff(5937,plain,
% 1.74/1.90 (~(z = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4411, 5935])).
% 1.74/1.90 tff(5938,plain,
% 1.74/1.90 (~b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5707, 5937, 984, 276, 1301, 247, 5936, 172, 2520, 215])).
% 1.74/1.90 tff(5939,plain,
% 1.74/1.90 (r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[963, 5938])).
% 1.74/1.90 tff(5940,plain,
% 1.74/1.90 (r(elem!1, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[322, 4370, 247])).
% 1.74/1.90 tff(5941,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[317, 189, 5936, 5940, 5939])).
% 1.74/1.90 tff(5942,plain,(b(elem!1, s(z)) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(z))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5943,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5942, 276, 1301, 172, 247, 4858, 2520, 215, 4370])).
% 1.74/1.90 tff(5944,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5945,plain,
% 1.74/1.90 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), 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(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5946,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5945])).
% 1.74/1.90 tff(5947,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5946, 5944])).
% 1.74/1.90 tff(5948,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5949,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5948, 5947])).
% 1.74/1.90 tff(5950,plain,
% 1.74/1.90 (~b(s(elem!1), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5949, 337, 5943, 2520, 791, 5934])).
% 1.74/1.90 tff(5951,plain,
% 1.74/1.90 (r(s(elem!1), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[898, 5950, 50])).
% 1.74/1.90 tff(5952,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5824, 337, 5943, 2520, 5934])).
% 1.74/1.90 tff(5953,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[579, 5952, 428])).
% 1.74/1.90 tff(5954,plain,
% 1.74/1.90 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5423, 337, 5943, 791, 5934])).
% 1.74/1.90 tff(5955,plain,
% 1.74/1.90 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1970, 5954])).
% 1.74/1.90 tff(5956,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5433, 5955, 5953, 5951])).
% 1.74/1.90 tff(5957,plain,((s(s(s(elem!1))) = elem!1) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z)) | b(elem!1, z) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5958,plain,
% 1.74/1.90 (s(s(s(elem!1))) = elem!1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5957, 791, 2520, 50, 1301, 172, 247, 4858, 215, 4370])).
% 1.74/1.90 tff(5959,plain,
% 1.74/1.90 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5958])).
% 1.74/1.90 tff(5960,plain,
% 1.74/1.90 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5959, 5931])).
% 1.74/1.90 tff(5961,plain,
% 1.74/1.90 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5960])).
% 1.74/1.90 tff(5962,plain,
% 1.74/1.90 (~(elem!1 = s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2451, 5961])).
% 1.74/1.90 tff(5963,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3916, 189, 777, 118])).
% 1.74/1.90 tff(5964,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5965,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5966,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 1.74/1.90 tff(5967,plain,
% 1.74/1.90 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5966, 43, 5963])).
% 1.74/1.90 tff(5968,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5967, 5962])).
% 1.74/1.90 tff(5969,plain,
% 1.74/1.90 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5959])).
% 1.74/1.90 tff(5970,plain,
% 1.74/1.90 (~(s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2451, 5969])).
% 1.74/1.90 tff(5971,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2463, 5970, 4938])).
% 1.74/1.90 tff(5972,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5973,plain,
% 1.74/1.90 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5974,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5973])).
% 1.74/1.90 tff(5975,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5974, 5972])).
% 1.74/1.90 tff(5976,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5977,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5976, 5975])).
% 1.74/1.91 tff(5978,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5977, 337, 2520, 5971, 5968])).
% 1.74/1.91 tff(5979,plain,
% 1.74/1.91 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[4598])).
% 1.74/1.91 tff(5980,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5979])).
% 1.74/1.91 tff(5981,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[5980])).
% 1.74/1.91 tff(5982,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5979])).
% 1.74/1.91 tff(5983,plain,
% 1.74/1.91 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5982])).
% 1.74/1.91 tff(5984,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4598])).
% 1.74/1.91 tff(5985,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2510, 2502, 50])).
% 1.74/1.91 tff(5986,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[857, 5985, 229])).
% 1.74/1.91 tff(5987,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1177, 5986, 274])).
% 1.74/1.91 tff(5988,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1792, 5987])).
% 1.74/1.91 tff(5989,plain,
% 1.74/1.91 (b(s(s(elem!1)), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5988, 5984])).
% 1.74/1.91 tff(5990,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5991,plain,
% 1.74/1.91 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5992,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5991])).
% 1.74/1.91 tff(5993,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5992, 5990])).
% 1.74/1.91 tff(5994,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5995,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 1.74/1.91 tff(5996,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5995, 337, 600, 2520, 791, 5207, 5989])).
% 1.74/1.91 tff(5997,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5996, 5983])).
% 1.74/1.91 tff(5998,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[851, 5997])).
% 1.74/1.91 tff(5999,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5998, 5981])).
% 1.74/1.91 tff(6000,plain,
% 1.74/1.91 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5979])).
% 1.74/1.91 tff(6001,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[6000])).
% 1.74/1.91 tff(6002,plain,
% 1.74/1.91 (r(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5986, 6001])).
% 1.74/1.91 tff(6003,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6004,plain,
% 1.74/1.91 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6005,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6004])).
% 1.74/1.91 tff(6006,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6005, 6003])).
% 1.74/1.91 tff(6007,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6008,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6007, 6006])).
% 1.74/1.91 tff(6009,plain,
% 1.74/1.91 (~r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6008, 189, 777, 6002])).
% 1.74/1.91 tff(6010,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6009, 5999])).
% 1.74/1.91 tff(6011,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(elem!1, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6012,plain,
% 1.74/1.91 (~(s(s(s(z))) = s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6011, 791, 600, 2520, 777, 5284, 229, 50])).
% 1.74/1.91 tff(6013,plain,
% 1.74/1.91 (r(s(s(s(z))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4678, 43, 6012, 5978])).
% 1.74/1.91 tff(6014,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6015,plain,
% 1.74/1.91 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6016,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6015])).
% 1.74/1.91 tff(6017,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6016, 6014])).
% 1.74/1.91 tff(6018,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6019,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6018, 6017])).
% 1.74/1.91 tff(6020,plain,
% 1.74/1.91 (~b(s(elem!1), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6019, 337, 2520, 791, 5971, 5968])).
% 1.74/1.91 tff(6021,plain,
% 1.74/1.91 (r(s(elem!1), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[898, 6020, 50])).
% 1.74/1.91 tff(6022,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4845, 189, 6021, 118, 6013])).
% 1.74/1.91 tff(6023,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z)) | b(elem!1, z) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (~b(z, s(elem!1))) | (~r(elem!1, s(z))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6024,plain,
% 1.74/1.91 (b(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6023, 5929, 50, 5600, 5283, 172, 247, 4858, 147, 49, 600, 5916, 229])).
% 1.74/1.91 tff(6025,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5572, 6024, 3])).
% 1.74/1.91 tff(6026,plain,
% 1.74/1.91 (~r(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3923, 189, 5916, 49])).
% 1.74/1.91 tff(6027,plain,
% 1.74/1.91 (~(s(s(s(z))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1472, 6025])).
% 1.74/1.91 tff(6028,plain,
% 1.74/1.91 (b(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2463, 6027, 6026])).
% 1.74/1.91 tff(6029,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5707, 276, 215, 1301, 65, 1, 274, 247, 2520, 172])).
% 1.74/1.91 tff(6030,plain,
% 1.74/1.91 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[345, 6029, 327, 5689])).
% 1.74/1.91 tff(6031,plain,
% 1.74/1.91 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5465, 6029, 2470, 791, 327, 2454])).
% 1.74/1.91 tff(6032,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1970, 6031, 6030])).
% 1.74/1.91 tff(6033,plain,((s(s(s(elem!1))) = elem!1) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (z = elem!1) | (~b(s(z), z)) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6034,plain,
% 1.74/1.91 (s(s(s(elem!1))) = elem!1),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6033, 5929, 2451, 6024, 6028, 147, 5283, 61, 5918, 5284, 247, 5600, 172])).
% 1.74/1.91 tff(6035,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[801, 6034, 247])).
% 1.74/1.91 tff(6036,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[857, 6035, 229])).
% 1.74/1.91 tff(6037,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1177, 6036, 5284])).
% 1.74/1.91 tff(6038,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1792, 6037])).
% 1.74/1.91 tff(6039,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6040,plain,
% 1.74/1.91 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, 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(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6041,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6040])).
% 1.74/1.91 tff(6042,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6041, 6039])).
% 1.74/1.91 tff(6043,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6044,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6043, 6042])).
% 1.74/1.91 tff(6045,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6044, 337, 600, 5600, 5929, 5918, 6038])).
% 1.74/1.91 tff(6046,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[851, 6045])).
% 1.74/1.91 tff(6047,plain,
% 1.74/1.91 (~r(s(elem!1), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5630, 6046, 229, 5284, 5600, 6024, 600, 5283, 6025, 49, 50])).
% 1.74/1.91 tff(6048,plain,
% 1.74/1.91 (b(s(elem!1), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[898, 6047, 50])).
% 1.74/1.91 tff(6049,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6050,plain,
% 1.74/1.91 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6051,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6050])).
% 1.74/1.91 tff(6052,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6051, 6049])).
% 1.74/1.91 tff(6053,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6054,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6053, 6052])).
% 1.74/1.91 tff(6055,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6054, 337, 600, 6048, 5918, 5283])).
% 1.74/1.91 tff(6056,plain,((~b(z, s(elem!1))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(z))), s(z)) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6057,plain,
% 1.74/1.91 (~b(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6056, 4858, 229, 247, 172, 3, 50, 82, 370])).
% 1.74/1.91 tff(6058,plain,
% 1.74/1.91 (r(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[395, 6057])).
% 1.74/1.91 tff(6059,plain,
% 1.74/1.91 (~r(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1748, 6058, 370])).
% 1.74/1.91 tff(6060,plain,
% 1.74/1.91 (b(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[270, 6059, 265])).
% 1.74/1.91 tff(6061,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2530, 6060, 147, 172, 5284, 981, 6058])).
% 1.74/1.91 tff(6062,plain,
% 1.74/1.91 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5680, 6061])).
% 1.74/1.91 tff(6063,plain,
% 1.74/1.91 (s(s(s(elem!1))) = elem!1),
% 1.74/1.91 inference(symmetry,[status(thm)],[6062])).
% 1.74/1.91 tff(6064,plain,
% 1.74/1.91 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6063])).
% 1.74/1.91 tff(6065,plain,
% 1.74/1.91 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6064])).
% 1.74/1.91 tff(6066,plain,
% 1.74/1.91 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6062])).
% 1.74/1.91 tff(6067,plain,
% 1.74/1.91 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[6066])).
% 1.74/1.91 tff(6068,plain,
% 1.74/1.91 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6067])).
% 1.74/1.91 tff(6069,plain,
% 1.74/1.91 (~(s(s(s(z))) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2451, 6068])).
% 1.74/1.91 tff(6070,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6063])).
% 1.74/1.91 tff(6071,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6070])).
% 1.74/1.91 tff(6072,plain,
% 1.74/1.91 (s(s(s(elem!1))) = elem!1),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[281, 6062])).
% 1.74/1.91 tff(6073,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[801, 6072, 247])).
% 1.74/1.91 tff(6074,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[857, 6073, 229])).
% 1.74/1.91 tff(6075,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6074, 6071])).
% 1.74/1.91 tff(6076,plain,
% 1.74/1.91 (~r(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2617, 6075])).
% 1.74/1.91 tff(6077,plain,
% 1.74/1.91 (b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1786, 6076])).
% 1.74/1.91 tff(6078,plain,
% 1.74/1.91 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.74/1.91 inference(commutativity,[status(thm)],[])).
% 1.74/1.91 tff(6079,plain,
% 1.74/1.91 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6078])).
% 1.74/1.91 tff(6080,plain,
% 1.74/1.91 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6079])).
% 1.74/1.91 tff(6081,plain,
% 1.74/1.91 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[135, 6080])).
% 1.74/1.91 tff(6082,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6063])).
% 1.74/1.91 tff(6083,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6082])).
% 1.74/1.91 tff(6084,plain,
% 1.74/1.91 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6062])).
% 1.74/1.91 tff(6085,plain,
% 1.74/1.91 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[6084])).
% 1.74/1.91 tff(6086,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6062, 6085])).
% 1.74/1.91 tff(6087,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6086])).
% 1.74/1.91 tff(6088,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1082, 6058, 147])).
% 1.74/1.91 tff(6089,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[363, 6088, 172])).
% 1.74/1.91 tff(6090,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6089, 6087])).
% 1.74/1.91 tff(6091,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6090, 6083])).
% 1.74/1.91 tff(6092,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6063])).
% 1.74/1.92 tff(6093,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6092])).
% 1.74/1.92 tff(6094,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6085, 6062])).
% 1.74/1.92 tff(6095,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[6094])).
% 1.74/1.92 tff(6096,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2654, 6072, 6060])).
% 1.74/1.92 tff(6097,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6096, 6095])).
% 1.74/1.92 tff(6098,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6097, 6093])).
% 1.74/1.92 tff(6099,plain,
% 1.74/1.92 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6062])).
% 1.74/1.92 tff(6100,plain,
% 1.74/1.92 (b(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5928, 6059, 247, 172, 82, 4858, 5283, 5284, 370, 229])).
% 1.74/1.92 tff(6101,plain,
% 1.74/1.92 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6100, 6099])).
% 1.74/1.92 tff(6102,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6103,plain,
% 1.74/1.92 (((~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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(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(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(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(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6104,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), 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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6103])).
% 1.74/1.92 tff(6105,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), 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(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6104, 6102])).
% 1.74/1.92 tff(6106,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6107,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 1.74/1.92 tff(6108,plain,
% 1.74/1.92 ((~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(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6107, 337, 6101])).
% 1.74/1.92 tff(6109,plain,
% 1.74/1.92 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6108, 6098, 6091])).
% 1.74/1.92 tff(6110,plain,
% 1.74/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6111,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6112,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6111, 6110])).
% 1.74/1.92 tff(6113,plain,
% 1.74/1.92 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6112, 43, 6109])).
% 1.74/1.92 tff(6114,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6113, 6081])).
% 1.74/1.92 tff(6115,plain,
% 1.74/1.92 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6084])).
% 1.74/1.92 tff(6116,plain,
% 1.74/1.92 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6058, 6115])).
% 1.74/1.92 tff(6117,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6118,plain,
% 1.74/1.92 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6119,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6118])).
% 1.74/1.92 tff(6120,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6119, 6117])).
% 1.74/1.92 tff(6121,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6122,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6121, 6120])).
% 1.74/1.92 tff(6123,plain,
% 1.74/1.92 (~r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6122, 189, 6116, 6114])).
% 1.74/1.92 tff(6124,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[963, 6123])).
% 1.74/1.92 tff(6125,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1177, 6074, 5284])).
% 1.74/1.92 tff(6126,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1792, 6125])).
% 1.74/1.92 tff(6127,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6128,plain,
% 1.74/1.92 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~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(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6129,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6128])).
% 1.74/1.92 tff(6130,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6129, 6127])).
% 1.74/1.92 tff(6131,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6132,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6131, 6130])).
% 1.74/1.92 tff(6133,plain,
% 1.74/1.92 ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6132, 337, 5283, 6101, 6126])).
% 1.74/1.92 tff(6134,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6133, 6124])).
% 1.74/1.92 tff(6135,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[851, 6134])).
% 1.74/1.92 tff(6136,plain,
% 1.74/1.92 (~b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4313, 6135, 5283, 6124, 6077])).
% 1.74/1.92 tff(6137,plain,
% 1.74/1.92 (r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1498, 6136])).
% 1.74/1.92 tff(6138,plain,
% 1.74/1.92 (~r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4211, 6137, 370])).
% 1.74/1.92 tff(6139,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2463, 6138, 6069])).
% 1.74/1.92 tff(6140,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6139, 6065])).
% 1.74/1.92 tff(6141,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6085])).
% 1.74/1.92 tff(6142,plain,
% 1.74/1.92 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6141])).
% 1.74/1.92 tff(6143,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6085])).
% 1.74/1.92 tff(6144,plain,
% 1.74/1.92 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6143])).
% 1.74/1.92 tff(6145,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(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))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6146,plain,
% 1.74/1.92 (((~b(s(s(s(s(elem!1)))), 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(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))), s(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))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6147,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, 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(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)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6146])).
% 1.74/1.92 tff(6148,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, 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(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))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6147, 6145])).
% 1.74/1.92 tff(6149,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6150,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6149, 6148])).
% 1.74/1.92 tff(6151,plain,
% 1.74/1.92 ((~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(s(elem!1)))), s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6150, 337, 6101])).
% 1.74/1.92 tff(6152,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6151, 6098, 6091])).
% 1.74/1.92 tff(6153,plain,
% 1.74/1.92 (~b(s(elem!1), s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6152, 6144])).
% 1.74/1.92 tff(6154,plain,
% 1.74/1.92 (r(s(elem!1), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[898, 6153, 50])).
% 1.74/1.92 tff(6155,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6154, 6142])).
% 1.74/1.92 tff(6156,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6157,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6158,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 1.74/1.92 tff(6159,plain,
% 1.74/1.92 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6158, 189, 49])).
% 1.74/1.92 tff(6160,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6159, 6155])).
% 1.74/1.92 tff(6161,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3252, 6160])).
% 1.74/1.92 tff(6162,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6163,plain,
% 1.74/1.92 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6164,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6163])).
% 1.74/1.92 tff(6165,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6164, 6162])).
% 1.74/1.92 tff(6166,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6167,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 1.74/1.92 tff(6168,plain,
% 1.74/1.92 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6167, 189, 49])).
% 1.74/1.92 tff(6169,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6168, 6155])).
% 1.74/1.92 tff(6170,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1821, 6169])).
% 1.74/1.92 tff(6171,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6172,plain,
% 1.74/1.92 (((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6173,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6172])).
% 1.74/1.92 tff(6174,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6173, 6171])).
% 1.74/1.92 tff(6175,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6176,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6175, 6174])).
% 1.74/1.92 tff(6177,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6176, 337, 6170, 6161, 6091])).
% 1.74/1.92 tff(6178,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6177, 6140])).
% 1.74/1.92 tff(6179,plain,(b(elem!1, z) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6180,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6179, 370, 50, 229, 247, 172, 82, 3])).
% 1.74/1.92 tff(6181,plain,
% 1.74/1.92 (~r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3855, 1735, 370])).
% 1.74/1.93 tff(6182,plain,
% 1.74/1.93 (b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[963, 6181])).
% 1.74/1.93 tff(6183,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6184,plain,
% 1.74/1.93 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6185,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6184])).
% 1.74/1.93 tff(6186,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6185, 6183])).
% 1.74/1.93 tff(6187,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6188,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6187, 6186])).
% 1.74/1.93 tff(6189,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6188, 337, 1849, 2101, 6182, 1301, 790])).
% 1.74/1.93 tff(6190,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6191,plain,
% 1.74/1.93 (~r(s(z), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6190, 273, 50, 1301, 370])).
% 1.74/1.93 tff(6192,plain,
% 1.74/1.93 (b(s(z), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[727, 6191, 272])).
% 1.74/1.93 tff(6193,plain,
% 1.74/1.93 (~b(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3908, 6192, 1301, 1763])).
% 1.74/1.93 tff(6194,plain,
% 1.74/1.93 (r(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[322, 6193, 247])).
% 1.74/1.93 tff(6195,plain,
% 1.74/1.93 (~r(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2417, 6194, 273])).
% 1.74/1.93 tff(6196,plain,
% 1.74/1.93 (b(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[898, 6195, 50])).
% 1.74/1.93 tff(6197,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6198,plain,
% 1.74/1.93 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6199,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6198])).
% 1.74/1.93 tff(6200,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6199, 6197])).
% 1.74/1.93 tff(6201,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6202,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 1.74/1.93 tff(6203,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6202, 337, 1763, 1849, 6196, 6192, 1301, 790])).
% 1.74/1.93 tff(6204,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6205,plain,
% 1.74/1.93 (~r(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6204, 6180, 5283, 50, 247, 370])).
% 1.74/1.93 tff(6206,plain,
% 1.74/1.93 (b(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[270, 6205, 265])).
% 1.74/1.93 tff(6207,plain,
% 1.74/1.93 (~r(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6204, 1763, 1301, 50, 247, 370])).
% 1.74/1.93 tff(6208,plain,
% 1.74/1.93 (b(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[270, 6207, 265])).
% 1.74/1.93 tff(6209,plain,
% 1.74/1.93 (~(elem!1 = s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2754, 729])).
% 1.74/1.93 tff(6210,plain,
% 1.74/1.93 (b(s(z), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[727, 3856, 2754])).
% 1.74/1.93 tff(6211,plain,
% 1.74/1.93 (~b(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3908, 791, 1763, 1301])).
% 1.74/1.93 tff(6212,plain,
% 1.74/1.93 (r(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[322, 6211, 247])).
% 1.74/1.93 tff(6213,plain,
% 1.74/1.93 (~r(elem!1, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4434, 189, 6212, 788])).
% 1.74/1.93 tff(6214,plain,
% 1.74/1.93 (b(elem!1, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1015, 6213, 1008])).
% 1.74/1.93 tff(6215,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6216,plain,
% 1.74/1.93 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~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(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6217,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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(elem!1))) | (~b(s(z), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6216])).
% 1.74/1.93 tff(6218,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6217, 6215])).
% 1.74/1.93 tff(6219,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6220,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(z), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6219, 6218])).
% 1.74/1.93 tff(6221,plain,
% 1.74/1.93 (~b(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6220, 337, 2520, 791, 6214])).
% 1.74/1.93 tff(6222,plain,
% 1.74/1.93 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2133, 43, 6221])).
% 1.74/1.93 tff(6223,plain,
% 1.74/1.93 (r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6222, 4012])).
% 1.74/1.93 tff(6224,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6225,plain,
% 1.74/1.93 (((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6226,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6225])).
% 1.74/1.93 tff(6227,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6226, 6224])).
% 1.74/1.93 tff(6228,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6229,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6228, 6227])).
% 1.74/1.93 tff(6230,plain,
% 1.74/1.93 (~r(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6229, 189, 1077, 6223])).
% 1.74/1.93 tff(6231,plain,
% 1.74/1.93 (b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[963, 6230])).
% 1.74/1.93 tff(6232,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4379, 337, 1763, 791, 6231, 1301])).
% 1.74/1.93 tff(6233,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6234,plain,
% 1.74/1.93 (~r(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6233, 6210, 2520, 1763, 50, 1301, 1008, 1077, 6209])).
% 1.74/1.93 tff(6235,plain,
% 1.74/1.93 (b(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[898, 6234, 50])).
% 1.74/1.93 tff(6236,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6237,plain,
% 1.74/1.93 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~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))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6238,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6237])).
% 1.74/1.93 tff(6239,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6238, 6236])).
% 1.74/1.93 tff(6240,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6241,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6240, 6239])).
% 1.74/1.93 tff(6242,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6241, 337, 1763, 365, 326, 2520, 1544, 1301])).
% 1.74/1.93 tff(6243,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6244,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6243, 6235, 2520, 1301, 365, 1763])).
% 1.74/1.93 tff(6245,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6229, 189, 1077, 275, 5326])).
% 1.74/1.93 tff(6246,plain,((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6247,plain,
% 1.74/1.93 (~r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6246, 1077, 275])).
% 1.74/1.93 tff(6248,plain,
% 1.74/1.93 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2133, 43, 6247])).
% 1.74/1.93 tff(6249,plain,
% 1.74/1.93 (b(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6248, 4012])).
% 1.74/1.93 tff(6250,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6251,plain,
% 1.74/1.93 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6252,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6251])).
% 1.74/1.93 tff(6253,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6252, 6250])).
% 1.74/1.93 tff(6254,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6255,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6254, 6253])).
% 1.74/1.93 tff(6256,plain,
% 1.74/1.93 ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6255, 337, 1763, 2520, 6249])).
% 1.74/1.93 tff(6257,plain,
% 1.74/1.94 (~b(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6256, 6210])).
% 1.74/1.94 tff(6258,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[775])).
% 1.74/1.94 tff(6259,plain,
% 1.74/1.94 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6258])).
% 1.74/1.94 tff(6260,plain,
% 1.74/1.94 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6259])).
% 1.74/1.94 tff(6261,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1009, 6260])).
% 1.74/1.94 tff(6262,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[365, 6261])).
% 1.74/1.94 tff(6263,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6264,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6263, 6257, 365])).
% 1.74/1.94 tff(6265,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[350, 6264, 6244])).
% 1.74/1.94 tff(6266,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[752, 189, 370, 6265, 215])).
% 1.74/1.94 tff(6267,plain,((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (s(elem!1) = s(z)) | (elem!1 = s(elem!1)) | (~r(z, s(elem!1))) | (s(z) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6268,plain,
% 1.74/1.94 (~r(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6267, 1084, 215, 1301, 1763, 6208, 50, 981, 370, 272, 1077])).
% 1.74/1.94 tff(6269,plain,
% 1.74/1.94 (b(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[963, 6268])).
% 1.74/1.94 tff(6270,plain,
% 1.74/1.94 (~b(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4379, 337, 1763, 6269, 1301])).
% 1.74/1.94 tff(6271,plain,
% 1.74/1.94 (r(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[727, 6270, 272])).
% 1.74/1.94 tff(6272,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4119, 6271, 370])).
% 1.74/1.94 tff(6273,plain,
% 1.74/1.94 (s(s(s(s(z)))) = elem!1),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[857, 6272, 229])).
% 1.74/1.94 tff(6274,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6273])).
% 1.74/1.94 tff(6275,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2060, 6273, 6271, 118])).
% 1.74/1.94 tff(6276,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[548, 6275])).
% 1.74/1.94 tff(6277,plain,
% 1.74/1.94 (b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6276, 6274])).
% 1.74/1.94 tff(6278,plain,
% 1.74/1.94 (elem!1 = s(s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6273])).
% 1.74/1.94 tff(6279,plain,
% 1.74/1.94 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6278])).
% 1.74/1.94 tff(6280,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6279])).
% 1.74/1.94 tff(6281,plain,
% 1.74/1.94 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6278])).
% 1.74/1.94 tff(6282,plain,
% 1.74/1.94 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6281])).
% 1.74/1.94 tff(6283,plain,
% 1.74/1.94 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6284,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6283])).
% 1.74/1.94 tff(6285,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6284, 4092])).
% 1.74/1.94 tff(6286,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6287,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6286, 6285])).
% 1.74/1.94 tff(6288,plain,
% 1.74/1.94 (~b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6287, 337, 1763, 6269, 1301])).
% 1.74/1.94 tff(6289,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[322, 6288, 247])).
% 1.74/1.94 tff(6290,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3916, 189, 6289, 118])).
% 1.74/1.94 tff(6291,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6290, 6282])).
% 1.74/1.94 tff(6292,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[524, 6291])).
% 1.74/1.94 tff(6293,plain,
% 1.74/1.94 (b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6292, 6280])).
% 1.74/1.94 tff(6294,plain,
% 1.74/1.94 ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5977, 337, 6208, 6277])).
% 1.74/1.94 tff(6295,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6294, 6293])).
% 1.74/1.94 tff(6296,plain,
% 1.74/1.94 (~(s(s(s(z))) = s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2510, 6273, 50])).
% 1.74/1.94 tff(6297,plain,
% 1.74/1.94 (r(s(s(s(z))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4678, 43, 6296, 6295])).
% 1.74/1.94 tff(6298,plain,
% 1.74/1.94 (~r(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5020, 189, 1077, 6297])).
% 1.74/1.94 tff(6299,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1498, 6298])).
% 1.74/1.94 tff(6300,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5083, 337, 1763, 6269, 1301, 6299, 6277])).
% 1.74/1.94 tff(6301,plain,((~r(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6302,plain,
% 1.74/1.94 (~r(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6301, 6180, 5283, 49, 50, 229, 370, 247, 147, 172])).
% 1.74/1.94 tff(6303,plain,
% 1.74/1.94 (b(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[395, 6302])).
% 1.74/1.94 tff(6304,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6305,plain,
% 1.74/1.94 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6306,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6305])).
% 1.74/1.94 tff(6307,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6306, 6304])).
% 1.74/1.94 tff(6308,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6309,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.74/1.94 tff(6310,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6309, 337, 1763, 600, 2520, 982])).
% 1.74/1.94 tff(6311,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6312,plain,
% 1.74/1.94 (~b(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6311, 6303, 6180, 6206])).
% 1.74/1.94 tff(6313,plain,
% 1.74/1.94 (r(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1015, 6312, 981])).
% 1.74/1.94 tff(6314,plain,
% 1.74/1.94 (~b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6287, 337, 1763, 1, 1301])).
% 1.74/1.94 tff(6315,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[322, 6314, 247])).
% 1.74/1.94 tff(6316,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4434, 189, 2543, 777, 788])).
% 1.74/1.94 tff(6317,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6318,plain,
% 1.74/1.94 (~r(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6317, 6315, 2543])).
% 1.74/1.94 tff(6319,plain,
% 1.74/1.94 (b(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[898, 6318, 50])).
% 1.74/1.94 tff(6320,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6054, 337, 600, 6319, 1, 1301])).
% 1.74/1.94 tff(6321,plain,((~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6322,plain,
% 1.74/1.94 (~b(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6321, 6303, 5283, 50, 6313, 247, 6180])).
% 1.74/1.94 tff(6323,plain,
% 1.74/1.94 (r(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[963, 6322])).
% 1.74/1.94 tff(6324,plain,
% 1.74/1.94 (~r(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3855, 6323, 370])).
% 1.74/1.94 tff(6325,plain,
% 1.74/1.94 (b(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[727, 6324, 272])).
% 1.74/1.94 tff(6326,plain,
% 1.74/1.94 (~b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3908, 6325, 5283, 6180])).
% 1.74/1.94 tff(6327,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[322, 6326, 247])).
% 1.74/1.94 tff(6328,plain,
% 1.74/1.94 (~r(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6317, 6327, 6313])).
% 1.74/1.94 tff(6329,plain,
% 1.74/1.94 (b(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[898, 6328, 50])).
% 1.74/1.94 tff(6330,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6331,plain,
% 1.74/1.94 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6332,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6331])).
% 1.74/1.94 tff(6333,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6332, 6330])).
% 1.74/1.94 tff(6334,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6335,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6334, 6333])).
% 1.74/1.94 tff(6336,plain,
% 1.74/1.94 (~b(s(z), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6335, 337, 6180, 6206, 6329, 6325, 5283])).
% 1.74/1.94 tff(6337,plain,
% 1.74/1.94 (r(s(z), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2133, 43, 6336, 55])).
% 1.74/1.94 tff(6338,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5375, 189, 6313, 6327, 6337])).
% 1.74/1.94 tff(6339,plain,((~r(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6340,plain,
% 1.74/1.94 (~r(z, elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6339, 247, 50, 229, 172, 82, 3])).
% 1.74/1.94 tff(6341,plain,
% 1.74/1.94 (b(z, elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[921, 6340, 61])).
% 1.74/1.94 tff(6342,plain,
% 1.74/1.94 (~r(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5227, 5940, 1301, 50, 5284, 925])).
% 1.74/1.94 tff(6343,plain,
% 1.74/1.94 (b(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[270, 6342, 265])).
% 1.74/1.94 tff(6344,plain,
% 1.74/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[295, 43, 5932, 282])).
% 1.74/1.94 tff(6345,plain,
% 1.74/1.94 (~r(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2530, 6343, 215, 172, 5284, 981, 6344])).
% 1.74/1.94 tff(6346,plain,
% 1.74/1.94 (b(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[395, 6345])).
% 1.74/1.94 tff(6347,plain,
% 1.74/1.94 (~b(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2540, 6346, 925, 6343])).
% 1.74/1.94 tff(6348,plain,
% 1.74/1.94 (r(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1015, 6347, 981])).
% 1.74/1.94 tff(6349,plain,
% 1.74/1.94 (~r(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1023, 6348, 5284])).
% 1.74/1.94 tff(6350,plain,
% 1.74/1.94 (b(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[378, 43, 114, 6349])).
% 1.74/1.94 tff(6351,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5942, 6343, 1301, 172, 247, 276, 4858, 215, 4370])).
% 1.74/1.94 tff(6352,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6353,plain,
% 1.74/1.94 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6354,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(X1, 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), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6353])).
% 1.74/1.94 tff(6355,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(X1, 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), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6354, 6352])).
% 1.74/1.94 tff(6356,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6357,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6356, 6355])).
% 1.74/1.94 tff(6358,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6357, 337, 925, 6351, 6343, 6344, 6350])).
% 1.74/1.94 tff(6359,plain,(b(elem!1, s(z)) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | b(elem!1, z) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6360,plain,
% 1.74/1.94 (b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6359, 4858, 147, 172, 5283, 247, 1712, 925, 50])).
% 1.74/1.94 tff(6361,plain,
% 1.74/1.94 (~b(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2563, 6360, 172, 925, 5284, 82])).
% 1.74/1.94 tff(6362,plain,
% 1.74/1.94 (r(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[270, 6361, 265])).
% 1.74/1.94 tff(6363,plain,
% 1.74/1.94 (~b(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5598, 6362, 172, 82, 4858, 247, 3, 50])).
% 1.74/1.94 tff(6364,plain,
% 1.74/1.94 (r(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[395, 6363])).
% 1.74/1.94 tff(6365,plain,
% 1.74/1.94 (~r(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1032, 6364, 5284])).
% 1.74/1.94 tff(6366,plain,
% 1.74/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[295, 43, 5679, 1713])).
% 1.74/1.94 tff(6367,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[972, 6360, 925, 6366])).
% 1.74/1.94 tff(6368,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[350, 6367, 1712])).
% 1.74/1.94 tff(6369,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[358, 6368, 6362])).
% 1.74/1.94 tff(6370,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[363, 6369, 172])).
% 1.74/1.94 tff(6371,plain,
% 1.74/1.94 (~b(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1006, 6370, 6362, 5679, 428, 1712, 6367])).
% 1.74/1.94 tff(6372,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1015, 6371, 6365, 981])).
% 1.74/1.94 tff(6373,plain,(b(elem!1, z) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(z)) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6374,plain,
% 1.74/1.94 (b(elem!1, z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6373, 247, 82, 172, 3, 50, 6341])).
% 1.74/1.94 tff(6375,plain,
% 1.74/1.94 (~b(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4005, 6374, 5283, 6341])).
% 1.74/1.94 tff(6376,plain,
% 1.74/1.94 (r(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[727, 6375, 272])).
% 1.74/1.94 tff(6377,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[928, 6341, 82])).
% 1.74/1.94 tff(6378,plain,
% 1.74/1.94 (~b(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4005, 1763, 1301, 925])).
% 1.74/1.94 tff(6379,plain,
% 1.74/1.94 (r(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[727, 6378, 272])).
% 1.74/1.94 tff(6380,plain,
% 1.74/1.94 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.94 inference(commutativity,[status(thm)],[])).
% 1.74/1.94 tff(6381,plain,
% 1.74/1.94 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6380])).
% 1.74/1.94 tff(6382,plain,
% 1.74/1.94 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6381])).
% 1.74/1.94 tff(6383,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2451, 6382])).
% 1.74/1.94 tff(6384,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6385,plain,
% 1.74/1.94 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6386,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6385])).
% 1.74/1.94 tff(6387,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6386, 6384])).
% 1.74/1.94 tff(6388,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6389,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6388, 6387])).
% 1.74/1.94 tff(6390,plain,
% 1.74/1.94 (~b(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6389, 337, 4069, 1301, 2134])).
% 1.74/1.94 tff(6391,plain,
% 1.74/1.94 (r(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[395, 6390])).
% 1.74/1.94 tff(6392,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1082, 6391, 215])).
% 1.74/1.94 tff(6393,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[363, 6392, 172])).
% 1.74/1.94 tff(6394,plain,
% 1.74/1.94 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6395,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6394])).
% 1.74/1.94 tff(6396,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6395, 2188])).
% 1.74/1.94 tff(6397,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6398,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 1.74/1.94 tff(6399,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6398, 337, 6393, 4069, 2134])).
% 1.74/1.94 tff(6400,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[227, 43, 6399, 213])).
% 1.74/1.95 tff(6401,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6402,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6403,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6402, 6401])).
% 1.74/1.95 tff(6404,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6403, 189, 6400, 118])).
% 1.74/1.95 tff(6405,plain,
% 1.74/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6406,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6407,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6406, 6405])).
% 1.74/1.95 tff(6408,plain,
% 1.74/1.95 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6407, 43, 6404])).
% 1.74/1.95 tff(6409,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6408, 6383])).
% 1.74/1.95 tff(6410,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6411,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6412,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6411, 6410])).
% 1.74/1.95 tff(6413,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6412, 189, 6400, 118])).
% 1.74/1.95 tff(6414,plain,
% 1.74/1.95 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2473, 43, 2451, 6413])).
% 1.74/1.95 tff(6415,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6416,plain,
% 1.74/1.95 (((~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(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6417,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6416])).
% 1.74/1.95 tff(6418,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6417, 6415])).
% 1.74/1.95 tff(6419,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6420,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6419, 6418])).
% 1.74/1.95 tff(6421,plain,
% 1.74/1.95 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6420, 189, 777, 6400])).
% 1.74/1.95 tff(6422,plain,
% 1.74/1.95 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[295, 43, 6421, 282])).
% 1.74/1.95 tff(6423,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6424,plain,
% 1.74/1.95 (((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6425,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6424])).
% 1.74/1.95 tff(6426,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6425, 6423])).
% 1.74/1.95 tff(6427,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6428,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6427, 6426])).
% 1.74/1.95 tff(6429,plain,
% 1.74/1.95 (~b(s(elem!1), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6428, 337, 4069, 1301, 2134])).
% 1.74/1.95 tff(6430,plain,
% 1.74/1.95 (r(s(elem!1), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[378, 43, 114, 6429])).
% 1.74/1.95 tff(6431,plain,
% 1.74/1.95 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1227, 6430, 215])).
% 1.74/1.95 tff(6432,plain,
% 1.74/1.95 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[579, 6431, 428])).
% 1.74/1.95 tff(6433,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6434,plain,
% 1.74/1.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6435,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6434])).
% 1.74/1.95 tff(6436,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6435, 6433])).
% 1.74/1.95 tff(6437,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6438,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6437, 6436])).
% 1.74/1.95 tff(6439,plain,
% 1.74/1.95 (~b(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6438, 337, 6393, 6432, 6422, 6414])).
% 1.74/1.95 tff(6440,plain,
% 1.74/1.95 (elem!1 = s(s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5967, 6439])).
% 1.74/1.95 tff(6441,plain,
% 1.74/1.95 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6440])).
% 1.74/1.95 tff(6442,plain,
% 1.74/1.95 (b(z, s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[925, 6441])).
% 1.74/1.95 tff(6443,plain,
% 1.74/1.95 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6440])).
% 1.74/1.95 tff(6444,plain,
% 1.74/1.95 (b(s(s(s(z))), z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1763, 6443])).
% 1.74/1.95 tff(6445,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6440])).
% 1.74/1.95 tff(6446,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6447,plain,
% 1.74/1.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1))) <=> ((~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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6448,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6447])).
% 1.74/1.95 tff(6449,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6448, 6446])).
% 1.74/1.95 tff(6450,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6451,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6450, 6449])).
% 1.74/1.95 tff(6452,plain,
% 1.74/1.95 (~b(s(s(s(z))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6451, 337, 6393, 6432, 6422, 6414])).
% 1.74/1.95 tff(6453,plain,
% 1.74/1.95 (s(s(s(z))) = elem!1),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2463, 6452, 4938])).
% 1.74/1.95 tff(6454,plain,
% 1.74/1.95 (s(s(s(s(z)))) = s(elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1472, 6453])).
% 1.74/1.95 tff(6455,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[809, 6454, 273])).
% 1.74/1.95 tff(6456,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6455, 6445])).
% 1.74/1.95 tff(6457,plain,
% 1.74/1.95 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6440])).
% 1.74/1.95 tff(6458,plain,
% 1.74/1.95 (r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1735, 6457])).
% 1.74/1.95 tff(6459,plain,
% 1.74/1.95 (s(elem!1) = s(s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6440])).
% 1.74/1.95 tff(6460,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6459])).
% 1.74/1.95 tff(6461,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6460, 681])).
% 1.74/1.95 tff(6462,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6461, 682])).
% 1.74/1.95 tff(6463,plain,
% 1.74/1.95 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6462])).
% 1.74/1.95 tff(6464,plain,
% 1.74/1.95 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4414, 6463])).
% 1.74/1.95 tff(6465,plain,
% 1.74/1.95 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6459])).
% 1.74/1.95 tff(6466,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4069, 6465])).
% 1.74/1.95 tff(6467,plain,
% 1.74/1.95 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2089, 6455, 1735])).
% 1.74/1.95 tff(6468,plain,
% 1.74/1.95 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1150, 6467])).
% 1.74/1.95 tff(6469,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6470,plain,
% 1.74/1.95 (((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6471,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6470])).
% 1.74/1.95 tff(6472,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~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(X1, 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(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6471, 6469])).
% 1.74/1.95 tff(6473,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6474,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.74/1.95 tff(6475,plain,
% 1.74/1.95 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6474, 337, 6393, 4069, 2134])).
% 1.74/1.95 tff(6476,plain,
% 1.74/1.95 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1970, 6475])).
% 1.74/1.95 tff(6477,plain,
% 1.74/1.95 (~r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[306, 6476, 215])).
% 1.74/1.95 tff(6478,plain,
% 1.74/1.95 (b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[963, 6477])).
% 1.74/1.95 tff(6479,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(6480,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(6481,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6482,plain,
% 1.74/1.95 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6483,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6482])).
% 1.74/1.95 tff(6484,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6483, 6481])).
% 1.74/1.95 tff(6485,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6486,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6485, 6484])).
% 1.74/1.95 tff(6487,plain,
% 1.74/1.95 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6486, 189, 6480, 6479])).
% 1.74/1.95 tff(6488,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4520, 43, 135, 6487])).
% 1.74/1.95 tff(6489,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(6490,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6491,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6492,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6491, 6490])).
% 1.74/1.96 tff(6493,plain,
% 1.74/1.96 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6492, 189, 6489, 6480])).
% 1.74/1.96 tff(6494,plain,
% 1.74/1.96 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[700, 6493, 3466])).
% 1.74/1.96 tff(6495,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6496,plain,
% 1.74/1.96 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~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), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6497,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6496])).
% 1.74/1.96 tff(6498,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6497, 6495])).
% 1.74/1.96 tff(6499,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~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))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6500,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6499, 6498])).
% 1.74/1.96 tff(6501,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6500, 337, 1, 1275, 1231, 6494, 6488])).
% 1.74/1.96 tff(6502,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6503,plain,
% 1.74/1.96 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6502, 6478, 6468, 6466, 6464, 6458, 6456])).
% 1.74/1.96 tff(6504,plain,
% 1.74/1.96 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3252, 6503])).
% 1.74/1.96 tff(6505,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6506,plain,
% 1.74/1.96 (((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6507,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6506])).
% 1.74/1.96 tff(6508,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6507, 6505])).
% 1.74/1.96 tff(6509,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6510,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 1.74/1.96 tff(6511,plain,
% 1.74/1.96 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6510, 337, 6504, 6444, 6442, 6409])).
% 1.74/1.96 tff(6512,plain,
% 1.74/1.96 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4497, 43, 3129, 6511])).
% 1.74/1.96 tff(6513,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6514,plain,
% 1.74/1.96 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6515,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6514])).
% 1.74/1.96 tff(6516,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6515, 6513])).
% 1.74/1.96 tff(6517,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6518,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6517, 6516])).
% 1.74/1.96 tff(6519,plain,
% 1.74/1.96 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6518, 337, 1301, 6504, 6444, 6442])).
% 1.74/1.96 tff(6520,plain,
% 1.74/1.96 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[663, 6519])).
% 1.74/1.96 tff(6521,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2166, 4069, 172, 1735, 273, 777])).
% 1.74/1.96 tff(6522,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[350, 6521, 276])).
% 1.74/1.96 tff(6523,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2174, 337, 925, 1763, 6522])).
% 1.74/1.96 tff(6524,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[406, 43, 133, 6523])).
% 1.74/1.96 tff(6525,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[678, 189, 6524, 6520, 6512])).
% 1.74/1.96 tff(6526,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6527,plain,
% 1.74/1.96 (~r(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6526, 5940, 6379, 1763, 925, 118, 1301, 215, 172, 276, 50])).
% 1.74/1.96 tff(6528,plain,
% 1.74/1.96 (b(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[270, 6527, 265])).
% 1.74/1.96 tff(6529,plain,
% 1.74/1.96 (~b(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2717, 6528, 925, 1763])).
% 1.74/1.96 tff(6530,plain,
% 1.74/1.96 (r(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[395, 6529])).
% 1.74/1.96 tff(6531,plain,
% 1.74/1.96 (b(s(elem!1), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5047, 6530, 247, 6527, 276, 215, 6378, 4370])).
% 1.74/1.96 tff(6532,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3968, 337, 925, 1763, 6528, 6531])).
% 1.74/1.96 tff(6533,plain,(b(elem!1, s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6534,plain,
% 1.74/1.96 (b(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6533, 6341, 6374, 247, 6377, 147, 49, 5283, 172, 50])).
% 1.74/1.96 tff(6535,plain,
% 1.74/1.96 (~r(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4077, 6341, 6534, 5283, 6376, 50])).
% 1.74/1.96 tff(6536,plain,
% 1.74/1.96 (b(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[270, 6535, 265])).
% 1.74/1.96 tff(6537,plain,
% 1.74/1.96 (~b(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2717, 6536, 6341, 6374])).
% 1.74/1.96 tff(6538,plain,
% 1.74/1.96 (r(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[395, 6537])).
% 1.74/1.96 tff(6539,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1082, 6538, 147])).
% 1.74/1.96 tff(6540,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[363, 6539, 172])).
% 1.74/1.96 tff(6541,plain,
% 1.74/1.96 (~b(s(elem!1), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3968, 337, 6341, 6374, 6536])).
% 1.74/1.96 tff(6542,plain,
% 1.74/1.96 (r(s(elem!1), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[378, 43, 114, 6541])).
% 1.74/1.96 tff(6543,plain,
% 1.74/1.96 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1227, 6542, 147])).
% 1.74/1.96 tff(6544,plain,
% 1.74/1.96 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[579, 6543, 428])).
% 1.74/1.96 tff(6545,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6546,plain,
% 1.74/1.96 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6547,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6546])).
% 1.74/1.96 tff(6548,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6547, 6545])).
% 1.74/1.96 tff(6549,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6550,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6549, 6548])).
% 1.74/1.96 tff(6551,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6550, 337, 925, 1763, 327, 1, 1301])).
% 1.74/1.96 tff(6552,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6553,plain,
% 1.74/1.96 (~b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6552, 6341, 6374, 6534, 5283])).
% 1.74/1.96 tff(6554,plain,
% 1.74/1.96 (r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[963, 6553])).
% 1.74/1.96 tff(6555,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4481, 6554, 50, 6542, 6544, 6540])).
% 1.74/1.96 tff(6556,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4024, 189, 1219, 788, 275])).
% 1.74/1.96 tff(6557,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6558,plain,
% 1.74/1.96 (~r(s(elem!1), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6557, 6554, 6542])).
% 1.74/1.96 tff(6559,plain,
% 1.74/1.96 (b(s(elem!1), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[898, 6558, 50])).
% 1.74/1.96 tff(6560,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6243, 6559, 5283, 6374, 6536, 6540])).
% 1.74/1.96 tff(6561,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[350, 6560, 6377])).
% 1.74/1.96 tff(6562,plain,
% 1.74/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6563,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6564,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6563, 6562])).
% 1.74/1.96 tff(6565,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6564, 189, 6561, 6376])).
% 1.74/1.96 tff(6566,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[227, 43, 6565, 6555, 213])).
% 1.74/1.96 tff(6567,plain,((elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(s(s(s(z))), s(z)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6568,plain,
% 1.74/1.96 (elem!1 = s(z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6567, 229, 172, 82, 3, 50])).
% 1.74/1.96 tff(6569,plain,
% 1.74/1.96 (s(elem!1) = s(s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6568])).
% 1.74/1.96 tff(6570,plain,
% 1.74/1.96 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6569])).
% 1.74/1.96 tff(6571,plain,
% 1.74/1.96 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6568])).
% 1.74/1.96 tff(6572,plain,
% 1.74/1.96 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6571, 6570])).
% 1.74/1.96 tff(6573,plain,
% 1.74/1.96 (r(z, elem!1) <=> r(z, s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6568])).
% 1.74/1.96 tff(6574,plain,
% 1.74/1.96 (r(z, s(z)) <=> r(z, elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6573])).
% 1.74/1.96 tff(6575,plain,
% 1.74/1.96 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6574])).
% 1.74/1.96 tff(6576,plain,
% 1.74/1.96 (~r(z, elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5282, 6575])).
% 1.74/1.96 tff(6577,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6569])).
% 1.74/1.96 tff(6578,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6577])).
% 1.74/1.96 tff(6579,plain,
% 1.74/1.96 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6578])).
% 1.74/1.96 tff(6580,plain,
% 1.74/1.96 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(s(s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6579])).
% 1.74/1.96 tff(6581,plain,
% 1.74/1.96 (~b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[82, 6580])).
% 1.74/1.96 tff(6582,plain,
% 1.74/1.96 (b(z, elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1301, 931])).
% 1.74/1.96 tff(6583,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.74/1.96 tff(6584,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6583, 6582])).
% 1.74/1.96 tff(6585,plain,((~(elem!1 = s(z))) | b(z, elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6586,plain,
% 1.74/1.96 (b(z, elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6585, 6568, 5283])).
% 1.74/1.96 tff(6587,plain,
% 1.74/1.96 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[928, 6586, 82])).
% 1.74/1.96 tff(6588,plain,
% 1.74/1.96 (r(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1759, 4858, 1900])).
% 1.74/1.96 tff(6589,plain,
% 1.74/1.96 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1268])).
% 1.74/1.96 tff(6590,plain,
% 1.74/1.96 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6589])).
% 1.74/1.96 tff(6591,plain,
% 1.74/1.96 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6590])).
% 1.74/1.96 tff(6592,plain,
% 1.74/1.96 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.74/1.96 inference(bind,[status(th)],[])).
% 1.74/1.96 tff(6593,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(quant_intro,[status(thm)],[6592])).
% 1.74/1.96 tff(6594,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6595,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.74/1.96 tff(6596,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6595, 6594])).
% 1.74/1.96 tff(6597,plain,(
% 1.74/1.96 ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(skolemize,[status(sab)],[6596])).
% 1.74/1.96 tff(6598,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6597, 6593])).
% 1.74/1.96 tff(6599,plain,
% 1.74/1.96 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6600,plain,
% 1.74/1.96 (~b(elem!1, elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6599, 6598])).
% 1.74/1.96 tff(6601,plain,
% 1.74/1.96 (~b(elem!1, s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6600, 6591])).
% 1.74/1.96 tff(6602,plain,
% 1.74/1.96 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1268])).
% 1.74/1.96 tff(6603,plain,
% 1.74/1.96 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6602])).
% 1.74/1.96 tff(6604,plain,
% 1.74/1.96 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6603])).
% 1.74/1.96 tff(6605,plain,
% 1.74/1.96 (~b(s(z), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6600, 6604])).
% 1.74/1.96 tff(6606,plain,
% 1.74/1.96 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[230])).
% 1.74/1.96 tff(6607,plain,
% 1.74/1.96 ((s(s(s(s(z)))) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6606, 843])).
% 1.74/1.96 tff(6608,plain,
% 1.74/1.96 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6607])).
% 1.74/1.96 tff(6609,plain,
% 1.74/1.96 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6608])).
% 1.74/1.96 tff(6610,plain,
% 1.74/1.96 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[516, 6609])).
% 1.74/1.96 tff(6611,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[857, 6610, 229])).
% 1.74/1.96 tff(6612,plain,
% 1.74/1.96 (r(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4920, 4858, 1301, 6611, 1784, 6605, 229, 6601, 2883])).
% 1.74/1.96 tff(6613,plain,
% 1.74/1.96 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3136])).
% 1.74/1.96 tff(6614,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[243, 230, 229])).
% 1.74/1.96 tff(6615,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6614, 6613])).
% 1.74/1.96 tff(6616,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[350, 6615, 276])).
% 1.74/1.97 tff(6617,plain,
% 1.74/1.97 (~b(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1212, 6588, 6616, 6612, 172, 230])).
% 1.74/1.97 tff(6618,plain,
% 1.74/1.97 (r(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[395, 6617])).
% 1.74/1.97 tff(6619,plain,
% 1.74/1.97 (~r(elem!1, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1032, 6618, 6588])).
% 1.74/1.97 tff(6620,plain,
% 1.74/1.97 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[291, 6588, 215])).
% 1.74/1.97 tff(6621,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[358, 6612, 6616])).
% 1.74/1.97 tff(6622,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[363, 6621, 172])).
% 1.74/1.97 tff(6623,plain,
% 1.74/1.97 (~b(elem!1, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1006, 6622, 6612, 6620, 428, 276, 6615])).
% 1.74/1.97 tff(6624,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1015, 6623, 6619, 981])).
% 1.74/1.97 tff(6625,plain,(b(elem!1, z) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6626,plain,
% 1.74/1.97 (b(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6625, 6587, 172, 6568, 147, 5283, 6581, 229, 6576, 68])).
% 1.74/1.97 tff(6627,plain,
% 1.74/1.97 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[281, 6587])).
% 1.74/1.97 tff(6628,plain,
% 1.74/1.97 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[632, 6627])).
% 1.74/1.97 tff(6629,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6568])).
% 1.74/1.97 tff(6630,plain,
% 1.74/1.97 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6629])).
% 1.74/1.97 tff(6631,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[229, 6630])).
% 1.74/1.97 tff(6632,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[851, 6631])).
% 1.74/1.97 tff(6633,plain,
% 1.74/1.97 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3040, 3039])).
% 1.74/1.97 tff(6634,plain,
% 1.74/1.97 (b(s(s(z)), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2520, 6633])).
% 1.74/1.97 tff(6635,plain,
% 1.74/1.97 (b(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6585, 230, 1301])).
% 1.74/1.97 tff(6636,plain,
% 1.74/1.97 (~b(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2717, 2520, 6635, 1763])).
% 1.74/1.97 tff(6637,plain,
% 1.74/1.97 (r(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[395, 6636])).
% 1.74/1.97 tff(6638,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1082, 6637, 215])).
% 1.74/1.97 tff(6639,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[363, 6638, 172])).
% 1.74/1.97 tff(6640,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6639, 1182])).
% 1.74/1.97 tff(6641,plain,
% 1.74/1.97 (r(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1108, 6637, 230])).
% 1.74/1.97 tff(6642,plain,
% 1.74/1.97 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1125, 6641, 230, 3048])).
% 1.74/1.97 tff(6643,plain,
% 1.74/1.97 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[579, 6642, 428])).
% 1.74/1.97 tff(6644,plain,
% 1.74/1.97 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1133, 6643, 230])).
% 1.74/1.97 tff(6645,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6646,plain,
% 1.74/1.97 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(s(z))), 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(s(z))), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6647,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(X1, 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(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(s(s(z))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6646])).
% 1.74/1.97 tff(6648,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(X1, 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(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(s(s(z)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6647, 6645])).
% 1.74/1.97 tff(6649,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6650,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6649, 6648])).
% 1.74/1.97 tff(6651,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6650, 337, 4944, 6644, 6640, 6634])).
% 1.74/1.97 tff(6652,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2854, 6651])).
% 1.74/1.97 tff(6653,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6654,plain,
% 1.74/1.97 (((~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))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6655,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6654])).
% 1.74/1.97 tff(6656,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6655, 6653])).
% 1.74/1.97 tff(6657,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6658,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6657, 6656])).
% 1.74/1.97 tff(6659,plain,
% 1.74/1.97 (~r(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6658, 189, 6641, 6652])).
% 1.74/1.97 tff(6660,plain,
% 1.74/1.97 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[199, 43, 6659])).
% 1.74/1.97 tff(6661,plain,
% 1.74/1.97 (b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6660, 179])).
% 1.74/1.97 tff(6662,plain,
% 1.74/1.97 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.74/1.97 inference(commutativity,[status(thm)],[])).
% 1.74/1.97 tff(6663,plain,
% 1.74/1.97 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[6662])).
% 1.74/1.97 tff(6664,plain,
% 1.74/1.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3107])).
% 1.74/1.97 tff(6665,plain,
% 1.74/1.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6664, 6663])).
% 1.74/1.97 tff(6666,plain,
% 1.74/1.97 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6665])).
% 1.74/1.97 tff(6667,plain,
% 1.74/1.97 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[116, 6666])).
% 1.74/1.97 tff(6668,plain,
% 1.74/1.97 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[1268])).
% 1.74/1.97 tff(6669,plain,
% 1.74/1.97 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.97 inference(symmetry,[status(thm)],[6668])).
% 1.74/1.97 tff(6670,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3107])).
% 1.74/1.97 tff(6671,plain,
% 1.74/1.97 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[3256])).
% 1.74/1.97 tff(6672,plain,
% 1.74/1.97 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[230])).
% 1.74/1.97 tff(6673,plain,
% 1.74/1.97 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6672, 6078])).
% 1.74/1.97 tff(6674,plain,
% 1.74/1.97 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[6673])).
% 1.74/1.97 tff(6675,plain,
% 1.74/1.97 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.97 inference(transitivity,[status(thm)],[6674, 6671])).
% 1.74/1.97 tff(6676,plain,
% 1.74/1.97 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6675])).
% 1.74/1.97 tff(6677,plain,
% 1.74/1.97 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[135, 6676])).
% 1.74/1.97 tff(6678,plain,
% 1.74/1.97 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[231])).
% 1.74/1.97 tff(6679,plain,
% 1.74/1.97 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.97 inference(symmetry,[status(thm)],[6678])).
% 1.74/1.97 tff(6680,plain,
% 1.74/1.97 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6679])).
% 1.74/1.97 tff(6681,plain,
% 1.74/1.97 (b(s(z), z) <=> b(elem!1, z)),
% 1.74/1.97 inference(symmetry,[status(thm)],[3103])).
% 1.74/1.97 tff(6682,plain,
% 1.74/1.97 ((~b(s(z), z)) <=> (~b(elem!1, z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6681])).
% 1.74/1.97 tff(6683,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.74/1.97 tff(6684,plain,
% 1.74/1.97 (~b(elem!1, z)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6683, 6682])).
% 1.74/1.97 tff(6685,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1763, 6684])).
% 1.74/1.97 tff(6686,plain,((~(elem!1 = s(z))) | (~b(elem!1, z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6687,plain,
% 1.74/1.97 (b(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6686, 1763, 230])).
% 1.74/1.97 tff(6688,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6689,plain,
% 1.74/1.97 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6690,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, 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)), s(z))) | (~b(s(s(z)), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6689])).
% 1.74/1.97 tff(6691,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, 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)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6690, 6688])).
% 1.74/1.97 tff(6692,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6693,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(z)), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6692, 6691])).
% 1.74/1.97 tff(6694,plain,
% 1.74/1.97 (~b(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6693, 337, 6687, 1301, 6634])).
% 1.74/1.97 tff(6695,plain,
% 1.74/1.97 (~b(s(elem!1), z)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6694, 6680])).
% 1.74/1.97 tff(6696,plain,
% 1.74/1.97 (r(s(elem!1), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1262, 6695, 230])).
% 1.74/1.97 tff(6697,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4470, 6696, 6635, 3949, 2520, 1763])).
% 1.74/1.97 tff(6698,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[714, 6697, 6677])).
% 1.74/1.97 tff(6699,plain,
% 1.74/1.97 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6698, 6670])).
% 1.74/1.97 tff(6700,plain,
% 1.74/1.97 (r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6699, 6669])).
% 1.74/1.97 tff(6701,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6702,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6703,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6702, 6701])).
% 1.74/1.97 tff(6704,plain,
% 1.74/1.97 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6703, 189, 118])).
% 1.74/1.97 tff(6705,plain,
% 1.74/1.97 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6704, 6700])).
% 1.74/1.97 tff(6706,plain,
% 1.74/1.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(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(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6707,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6708,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6707, 6706])).
% 1.74/1.97 tff(6709,plain,
% 1.74/1.97 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6708, 43])).
% 1.74/1.97 tff(6710,plain,
% 1.74/1.97 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6709, 6705, 6667])).
% 1.74/1.97 tff(6711,plain,
% 1.74/1.97 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3108])).
% 1.74/1.97 tff(6712,plain,
% 1.74/1.97 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6711, 681])).
% 1.74/1.97 tff(6713,plain,
% 1.74/1.97 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[6712])).
% 1.74/1.97 tff(6714,plain,
% 1.74/1.97 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6713])).
% 1.74/1.97 tff(6715,plain,
% 1.74/1.97 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3116])).
% 1.74/1.97 tff(6716,plain,
% 1.74/1.97 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3129, 6715])).
% 1.74/1.97 tff(6717,plain,
% 1.74/1.97 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6716, 6714])).
% 1.74/1.97 tff(6718,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6719,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6720,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6719, 6718])).
% 1.74/1.97 tff(6721,plain,
% 1.74/1.97 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6720, 189, 811])).
% 1.74/1.97 tff(6722,plain,
% 1.74/1.97 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6721, 6700])).
% 1.74/1.97 tff(6723,plain,
% 1.74/1.97 (((~![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))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6724,plain,
% 1.74/1.97 ((~![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))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6725,plain,
% 1.74/1.97 ((~![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)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6724, 6723])).
% 1.74/1.97 tff(6726,plain,
% 1.74/1.97 ((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)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6725, 43])).
% 1.74/1.97 tff(6727,plain,
% 1.74/1.97 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6726, 6722, 6717])).
% 1.74/1.97 tff(6728,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6729,plain,
% 1.74/1.97 (((~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(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6730,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6729])).
% 1.74/1.97 tff(6731,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6730, 6728])).
% 1.74/1.97 tff(6732,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6733,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6732, 6731])).
% 1.74/1.97 tff(6734,plain,
% 1.74/1.97 (~r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6733, 189, 6641, 6652])).
% 1.74/1.97 tff(6735,plain,
% 1.74/1.97 (b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1498, 6734])).
% 1.74/1.97 tff(6736,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6737,plain,
% 1.74/1.97 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6738,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6737])).
% 1.74/1.98 tff(6739,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6738, 6736])).
% 1.74/1.98 tff(6740,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6741,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6740, 6739])).
% 1.74/1.98 tff(6742,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6741, 337, 4946, 6735, 6727, 6710, 6661])).
% 1.74/1.98 tff(6743,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6744,plain,
% 1.74/1.98 (~b(s(elem!1), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6743, 6632, 49, 6568, 6628, 6626, 5283, 172, 147])).
% 1.74/1.98 tff(6745,plain,
% 1.74/1.98 (r(s(elem!1), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[270, 6744, 265])).
% 1.74/1.98 tff(6746,plain,
% 1.74/1.98 (r(s(s(z)), s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6745, 6572])).
% 1.74/1.98 tff(6747,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1293, 189, 49, 6746])).
% 1.74/1.98 tff(6748,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4268, 6747])).
% 1.74/1.98 tff(6749,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1198, 189, 6632, 6746])).
% 1.74/1.98 tff(6750,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2268, 6749])).
% 1.74/1.98 tff(6751,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3611, 189, 6632, 49])).
% 1.74/1.98 tff(6752,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[548, 6751])).
% 1.74/1.98 tff(6753,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4249, 189, 6632, 49])).
% 1.74/1.98 tff(6754,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[524, 6753])).
% 1.74/1.98 tff(6755,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4265, 337, 6754, 6752, 6750, 6748])).
% 1.74/1.98 tff(6756,plain,(b(s(s(s(s(z)))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | r(z, s(z)) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6757,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6756, 172, 82, 5282, 3, 50])).
% 1.74/1.98 tff(6758,plain,
% 1.74/1.98 (~b(z, elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6373, 247, 82, 172, 3, 50, 4858])).
% 1.74/1.98 tff(6759,plain,
% 1.74/1.98 (r(z, elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[921, 6758, 61])).
% 1.74/1.98 tff(6760,plain,
% 1.74/1.98 (~b(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5598, 273, 172, 82, 4858, 247, 3, 50])).
% 1.74/1.98 tff(6761,plain,
% 1.74/1.98 (~r(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1748, 273, 6759])).
% 1.74/1.98 tff(6762,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[395, 6761, 6760])).
% 1.74/1.98 tff(6763,plain,((~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(elem!1, z) | (elem!1 = s(z)) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6764,plain,
% 1.74/1.98 (~r(s(elem!1), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6763, 247, 82, 4858, 172, 3, 50])).
% 1.74/1.98 tff(6765,plain,
% 1.74/1.98 (~r(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3923, 189, 5940, 118])).
% 1.74/1.98 tff(6766,plain,
% 1.74/1.98 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2530, 1077, 215, 172, 5284, 981, 3079])).
% 1.74/1.98 tff(6767,plain,
% 1.74/1.98 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5933, 6766])).
% 1.74/1.98 tff(6768,plain,
% 1.74/1.98 (s(s(s(elem!1))) = elem!1),
% 1.74/1.98 inference(symmetry,[status(thm)],[6767])).
% 1.74/1.98 tff(6769,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6768])).
% 1.74/1.98 tff(6770,plain,
% 1.74/1.98 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6769])).
% 1.74/1.98 tff(6771,plain,
% 1.74/1.98 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6768])).
% 1.74/1.98 tff(6772,plain,
% 1.74/1.98 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6771])).
% 1.74/1.98 tff(6773,plain,
% 1.74/1.98 (~(s(s(s(z))) = elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2451, 6772])).
% 1.74/1.98 tff(6774,plain,
% 1.74/1.98 (b(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2463, 6773, 2461])).
% 1.74/1.98 tff(6775,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6774, 6770])).
% 1.74/1.98 tff(6776,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6768])).
% 1.74/1.98 tff(6777,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6776])).
% 1.74/1.98 tff(6778,plain,
% 1.74/1.98 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6767])).
% 1.74/1.98 tff(6779,plain,
% 1.74/1.98 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[6778])).
% 1.74/1.98 tff(6780,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6779, 6767])).
% 1.74/1.98 tff(6781,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[6780])).
% 1.74/1.98 tff(6782,plain,
% 1.74/1.98 (~r(elem!1, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1032, 1077, 5284])).
% 1.74/1.98 tff(6783,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3157, 6782, 3062, 1084, 265])).
% 1.74/1.98 tff(6784,plain,
% 1.74/1.98 (s(s(s(elem!1))) = elem!1),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5942, 6783, 1301, 172, 4858, 247, 3079, 215, 4370])).
% 1.74/1.98 tff(6785,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2654, 6784, 3079])).
% 1.74/1.98 tff(6786,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6785, 6781])).
% 1.74/1.98 tff(6787,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6786, 6777])).
% 1.74/1.98 tff(6788,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6768])).
% 1.74/1.98 tff(6789,plain,
% 1.74/1.98 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6788])).
% 1.74/1.98 tff(6790,plain,
% 1.74/1.98 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6767, 6779])).
% 1.74/1.98 tff(6791,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6790])).
% 1.74/1.98 tff(6792,plain,
% 1.74/1.98 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1084, 6791])).
% 1.74/1.98 tff(6793,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6792, 6789])).
% 1.74/1.98 tff(6794,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6795,plain,
% 1.74/1.98 (((~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(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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6796,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6795])).
% 1.74/1.98 tff(6797,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6796, 6794])).
% 1.74/1.98 tff(6798,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6799,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 1.74/1.98 tff(6800,plain,
% 1.74/1.98 ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6799, 337, 6793, 6787])).
% 1.74/1.98 tff(6801,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6800, 6775])).
% 1.74/1.98 tff(6802,plain,
% 1.74/1.98 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1821, 6801])).
% 1.74/1.98 tff(6803,plain,
% 1.74/1.98 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1466, 6784, 50])).
% 1.74/1.98 tff(6804,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6767])).
% 1.74/1.98 tff(6805,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1603, 6804])).
% 1.74/1.98 tff(6806,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(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(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6807,plain,
% 1.74/1.98 (((~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(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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), 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))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6808,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z)))), s(s(s(elem!1))))) | (~b(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(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6807])).
% 1.74/1.98 tff(6809,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z)))), s(s(s(elem!1))))) | (~b(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(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6808, 6806])).
% 1.74/1.98 tff(6810,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6811,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6810, 6809])).
% 1.74/1.98 tff(6812,plain,
% 1.74/1.98 ((~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(s(z)))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6811, 337, 6805])).
% 1.74/1.98 tff(6813,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6812, 6793, 6787])).
% 1.74/1.98 tff(6814,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1539, 6813, 6803])).
% 1.74/1.98 tff(6815,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6816,plain,
% 1.74/1.98 (((~b(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6817,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6816])).
% 1.74/1.98 tff(6818,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), 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))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6817, 6815])).
% 1.74/1.98 tff(6819,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6820,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6819, 6818])).
% 1.74/1.98 tff(6821,plain,
% 1.74/1.98 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6820, 337, 6805, 6793, 6787])).
% 1.74/1.98 tff(6822,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6821, 6775])).
% 1.74/1.98 tff(6823,plain,
% 1.74/1.98 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[548, 6822])).
% 1.74/1.98 tff(6824,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2683, 189, 6823, 6814, 6802])).
% 1.74/1.98 tff(6825,plain,((~r(z, s(elem!1))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, z) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6826,plain,
% 1.74/1.98 (~r(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6825, 3062, 1603, 50, 3844, 172, 4858, 247, 147, 4370, 6765])).
% 1.74/1.98 tff(6827,plain,
% 1.74/1.98 (b(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[395, 6826])).
% 1.74/1.98 tff(6828,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5942, 276, 1301, 172, 4858, 247, 2520, 215, 4370])).
% 1.74/1.98 tff(6829,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6830,plain,
% 1.74/1.98 (((~b(s(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(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(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))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6831,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(s(z)))), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6830])).
% 1.74/1.98 tff(6832,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6831, 6829])).
% 1.74/1.98 tff(6833,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6834,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6833, 6832])).
% 1.74/1.98 tff(6835,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6834, 337, 6828, 1603, 5934])).
% 1.74/1.98 tff(6836,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1947, 43, 2518, 6835])).
% 1.74/1.98 tff(6837,plain,
% 1.74/1.98 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5824, 337, 6828, 2520, 5934])).
% 1.74/1.98 tff(6838,plain,
% 1.74/1.98 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[579, 6837, 428])).
% 1.74/1.98 tff(6839,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6840,plain,
% 1.74/1.98 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6841,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6840])).
% 1.74/1.98 tff(6842,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6841, 6839])).
% 1.74/1.98 tff(6843,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6844,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6843, 6842])).
% 1.74/1.98 tff(6845,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6844, 189, 6838, 6836])).
% 1.74/1.98 tff(6846,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6847,plain,
% 1.74/1.99 (((~b(s(s(s(elem!1))), 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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6848,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(s(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(X1, 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), 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(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6847])).
% 1.74/1.99 tff(6849,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(s(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(X1, 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), 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(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6848, 6846])).
% 1.74/1.99 tff(6850,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(s(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))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6851,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6850, 6849])).
% 1.74/1.99 tff(6852,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6851, 337, 6828, 2520, 1603, 5934])).
% 1.74/1.99 tff(6853,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[832, 43, 6852])).
% 1.74/1.99 tff(6854,plain,
% 1.74/1.99 (s(s(s(s(z)))) = s(elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6853, 6845])).
% 1.74/1.99 tff(6855,plain,
% 1.74/1.99 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4552, 6854])).
% 1.74/1.99 tff(6856,plain,
% 1.74/1.99 (~b(s(z), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5957, 276, 2520, 50, 1301, 172, 247, 4858, 215, 4370])).
% 1.74/1.99 tff(6857,plain,
% 1.74/1.99 (r(s(z), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[727, 6856, 272])).
% 1.74/1.99 tff(6858,plain,
% 1.74/1.99 (~r(s(z), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3859, 5940, 5284])).
% 1.74/1.99 tff(6859,plain,
% 1.74/1.99 (b(s(z), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[963, 6858])).
% 1.74/1.99 tff(6860,plain,
% 1.74/1.99 (~r(s(elem!1), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1227, 6838, 215])).
% 1.74/1.99 tff(6861,plain,
% 1.74/1.99 (b(s(elem!1), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[378, 43, 114, 6860])).
% 1.74/1.99 tff(6862,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.74/1.99 tff(6863,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6864,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6865,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 1.74/1.99 tff(6866,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6865, 189, 1735, 6862])).
% 1.74/1.99 tff(6867,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4520, 43, 135, 6866])).
% 1.74/1.99 tff(6868,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6869,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6870,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6869, 6868])).
% 1.74/1.99 tff(6871,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6870, 189, 370, 6862])).
% 1.74/1.99 tff(6872,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[663, 6871])).
% 1.74/1.99 tff(6873,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6874,plain,
% 1.74/1.99 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6875,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6874])).
% 1.74/1.99 tff(6876,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6875, 6873])).
% 1.74/1.99 tff(6877,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6878,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 1.74/1.99 tff(6879,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6878, 337, 600, 1, 599, 6872, 6867])).
% 1.74/1.99 tff(6880,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(6881,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6880, 6861, 6859, 600, 6857, 370])).
% 1.74/1.99 tff(6882,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[714, 6881, 6855])).
% 1.74/1.99 tff(6883,plain,
% 1.74/1.99 (~b(s(elem!1), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5562, 337, 600, 6859, 6861])).
% 1.74/1.99 tff(6884,plain,
% 1.74/1.99 (r(s(elem!1), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[898, 6883, 50])).
% 1.74/1.99 tff(6885,plain,
% 1.74/1.99 (~r(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6317, 6884, 5940])).
% 1.74/1.99 tff(6886,plain,
% 1.74/1.99 (b(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1015, 6885, 981])).
% 1.74/1.99 tff(6887,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(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(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6888,plain,
% 1.74/1.99 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6889,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6888])).
% 1.74/1.99 tff(6890,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6889, 6887])).
% 1.74/1.99 tff(6891,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6892,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6891, 6890])).
% 1.74/1.99 tff(6893,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6892, 337, 6828, 2520, 6886, 6882])).
% 1.74/1.99 tff(6894,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4497, 43, 3129, 6893])).
% 1.74/1.99 tff(6895,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6896,plain,
% 1.74/1.99 (((~b(s(elem!1), elem!1)) | (~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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6897,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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(s(s(s(elem!1)))), s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6896])).
% 1.74/1.99 tff(6898,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6897, 6895])).
% 1.74/1.99 tff(6899,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6900,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6899, 6898])).
% 1.74/1.99 tff(6901,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6900, 337, 2520, 6886, 6882])).
% 1.74/1.99 tff(6902,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[649, 6901, 4414])).
% 1.74/1.99 tff(6903,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6904,plain,
% 1.74/1.99 (((~b(s(s(s(elem!1))), 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(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6905,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6904])).
% 1.74/1.99 tff(6906,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6905, 6903])).
% 1.74/1.99 tff(6907,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6908,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 1.74/1.99 tff(6909,plain,
% 1.74/1.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6908, 337, 6828, 2520, 5934])).
% 1.74/1.99 tff(6910,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[363, 6909, 172])).
% 1.74/1.99 tff(6911,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6912,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(6913,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[6912, 6911])).
% 1.74/1.99 tff(6914,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6913, 189, 6910, 6902, 6894])).
% 1.74/1.99 tff(6915,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(6916,plain,
% 1.74/1.99 (s(s(s(elem!1))) = elem!1),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6915, 3079, 6827, 370, 50, 147, 172, 1603, 3844, 247, 4858, 4370])).
% 1.74/1.99 tff(6917,plain,
% 1.74/1.99 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6916])).
% 1.74/1.99 tff(6918,plain,
% 1.74/1.99 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6917])).
% 1.74/1.99 tff(6919,plain,
% 1.74/1.99 (~(s(s(s(z))) = elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2451, 6918])).
% 1.74/1.99 tff(6920,plain,
% 1.74/1.99 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6917, 5931])).
% 1.74/1.99 tff(6921,plain,
% 1.74/1.99 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6920])).
% 1.74/1.99 tff(6922,plain,
% 1.74/1.99 (~(elem!1 = s(s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2451, 6921])).
% 1.74/1.99 tff(6923,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3916, 189, 5940, 118])).
% 1.74/1.99 tff(6924,plain,
% 1.74/1.99 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5966, 43, 6923])).
% 1.74/1.99 tff(6925,plain,
% 1.74/1.99 (b(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6924, 6922])).
% 1.74/1.99 tff(6926,plain,
% 1.74/1.99 (b(s(s(s(z))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2463, 6919, 6765])).
% 1.74/1.99 tff(6927,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6928,plain,
% 1.74/1.99 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(6929,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6928])).
% 1.74/1.99 tff(6930,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[6929, 6927])).
% 1.74/1.99 tff(6931,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(6932,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 1.74/2.00 tff(6933,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6932, 337, 1603, 6926, 6925])).
% 1.74/2.00 tff(6934,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[548, 6933])).
% 1.74/2.00 tff(6935,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2027, 6934, 118])).
% 1.74/2.00 tff(6936,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1150, 6935])).
% 1.74/2.00 tff(6937,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6938,plain,
% 1.74/2.00 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, 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(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6939,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[6938])).
% 1.74/2.00 tff(6940,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[6939, 6937])).
% 1.74/2.00 tff(6941,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(6942,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6941, 6940])).
% 1.74/2.00 tff(6943,plain,
% 1.74/2.00 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6942, 337, 6827, 3079, 6859, 1603])).
% 1.74/2.00 tff(6944,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6943, 6936])).
% 1.74/2.00 tff(6945,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1792, 6944])).
% 1.74/2.00 tff(6946,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6947,plain,
% 1.74/2.00 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6948,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[6947])).
% 1.74/2.00 tff(6949,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[6948, 6946])).
% 1.74/2.00 tff(6950,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(6951,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6950, 6949])).
% 1.74/2.00 tff(6952,plain,
% 1.74/2.00 (~b(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6951, 337, 6827, 3079, 3844, 6936, 1603])).
% 1.74/2.00 tff(6953,plain,
% 1.74/2.00 (r(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[898, 6952, 50])).
% 1.74/2.00 tff(6954,plain,
% 1.74/2.00 (~r(elem!1, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6317, 6953, 5940])).
% 1.74/2.00 tff(6955,plain,
% 1.74/2.00 (b(elem!1, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1015, 6954, 981])).
% 1.74/2.00 tff(6956,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1177, 6945, 5284])).
% 1.74/2.00 tff(6957,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4748, 6859, 370, 5940, 3844])).
% 1.74/2.00 tff(6958,plain,
% 1.74/2.00 (~r(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5810, 6945, 3844, 247, 6859, 981, 3079, 6916, 6957, 61, 6956, 82])).
% 1.74/2.00 tff(6959,plain,
% 1.74/2.00 (b(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1786, 6958])).
% 1.74/2.00 tff(6960,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, 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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6961,plain,
% 1.74/2.00 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6962,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[6961])).
% 1.74/2.00 tff(6963,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[6962, 6960])).
% 1.74/2.00 tff(6964,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~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)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(6965,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6964, 6963])).
% 1.74/2.00 tff(6966,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6965, 337, 3844, 6936, 1603, 6959])).
% 1.74/2.00 tff(6967,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[851, 6966])).
% 1.74/2.00 tff(6968,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4313, 6967, 3844, 6859, 6959])).
% 1.74/2.00 tff(6969,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1498, 6968])).
% 1.74/2.00 tff(6970,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5796, 6969, 6955, 1603, 3079, 6945, 6919, 370])).
% 1.74/2.00 tff(6971,plain,(r(s(elem!1), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | b(z, s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(6972,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6971, 6764, 6759, 50, 247, 82, 49, 172, 4858, 1603])).
% 1.74/2.00 tff(6973,plain,
% 1.74/2.00 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5572, 6972, 3])).
% 1.74/2.00 tff(6974,plain,
% 1.74/2.00 (~(s(s(s(z))) = elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1472, 6973])).
% 1.74/2.00 tff(6975,plain,
% 1.74/2.00 (b(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[270, 6764, 265])).
% 1.74/2.00 tff(6976,plain,
% 1.74/2.00 (~r(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3855, 275, 370])).
% 1.74/2.00 tff(6977,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[727, 6976, 272])).
% 1.74/2.00 tff(6978,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[864, 337, 327, 6977, 1603])).
% 1.74/2.00 tff(6979,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[851, 6978])).
% 1.74/2.00 tff(6980,plain,
% 1.74/2.00 (~r(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3859, 275, 274])).
% 1.74/2.00 tff(6981,plain,
% 1.74/2.00 (~b(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2594, 6976, 247, 2520, 6980])).
% 1.74/2.00 tff(6982,plain,
% 1.74/2.00 (r(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[898, 6981, 50])).
% 1.74/2.00 tff(6983,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[827, 189, 6982, 6979])).
% 1.74/2.00 tff(6984,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6985,plain,
% 1.74/2.00 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6986,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[6985])).
% 1.74/2.00 tff(6987,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[6986, 6984])).
% 1.74/2.00 tff(6988,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(6989,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6988, 6987])).
% 1.74/2.00 tff(6990,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6989, 337, 327, 2520, 6977, 1603])).
% 1.74/2.00 tff(6991,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[832, 43, 829, 6990, 6983])).
% 1.74/2.00 tff(6992,plain,((~r(s(z), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(6993,plain,
% 1.74/2.00 (~r(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6992, 6973, 6972, 6975, 1603, 50, 247, 5284, 6759])).
% 1.74/2.00 tff(6994,plain,
% 1.74/2.00 (b(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[963, 6993])).
% 1.74/2.00 tff(6995,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6996,plain,
% 1.74/2.00 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6997,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[6996])).
% 1.74/2.00 tff(6998,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[6997, 6995])).
% 1.74/2.00 tff(6999,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7000,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 1.74/2.00 tff(7001,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7000, 337, 327, 2520, 1544, 1, 1301])).
% 1.74/2.00 tff(7002,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7003,plain,
% 1.74/2.00 (~b(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7002, 6972, 6975, 6994, 5283])).
% 1.74/2.00 tff(7004,plain,
% 1.74/2.00 (r(s(elem!1), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[898, 7003, 50])).
% 1.74/2.01 tff(7005,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5707, 276, 215, 1301, 65, 247, 2520, 274, 1, 172])).
% 1.74/2.01 tff(7006,plain,
% 1.74/2.01 (~b(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[345, 5689, 327, 7005])).
% 1.74/2.01 tff(7007,plain,
% 1.74/2.01 (r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1970, 7006])).
% 1.74/2.01 tff(7008,plain,
% 1.74/2.01 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5433, 7007, 788])).
% 1.74/2.01 tff(7009,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[579, 7008, 428])).
% 1.74/2.01 tff(7010,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7011,plain,
% 1.74/2.01 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~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(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(elem!1, s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7012,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7011])).
% 1.74/2.01 tff(7013,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7012, 7010])).
% 1.74/2.01 tff(7014,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~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)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7015,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 1.74/2.01 tff(7016,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7015, 337, 327, 7005, 2520, 7009, 5689])).
% 1.74/2.01 tff(7017,plain,((s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (z = elem!1) | (elem!1 = s(z)) | (~r(elem!1, z)) | (~b(s(z), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7018,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7017, 6972, 6975, 7004, 147, 5283, 61, 247, 5284, 6994, 172])).
% 1.74/2.01 tff(7019,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7018])).
% 1.74/2.01 tff(7020,plain,
% 1.74/2.01 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7019])).
% 1.74/2.01 tff(7021,plain,
% 1.74/2.01 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7020])).
% 1.74/2.01 tff(7022,plain,
% 1.74/2.01 (~(s(s(s(z))) = s(elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[116, 7021])).
% 1.74/2.01 tff(7023,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4845, 189, 7004, 49])).
% 1.74/2.01 tff(7024,plain,
% 1.74/2.01 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4678, 43, 7023])).
% 1.74/2.01 tff(7025,plain,
% 1.74/2.01 (b(s(s(s(z))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7024, 7022])).
% 1.74/2.01 tff(7026,plain,
% 1.74/2.01 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2530, 1077, 215, 172, 274, 981, 2520])).
% 1.74/2.01 tff(7027,plain,
% 1.74/2.01 (elem!1 = s(s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5688, 7026])).
% 1.74/2.01 tff(7028,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[281, 7027])).
% 1.74/2.01 tff(7029,plain,
% 1.74/2.01 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1466, 7028, 50])).
% 1.74/2.01 tff(7030,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(symmetry,[status(thm)],[7027])).
% 1.74/2.01 tff(7031,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7030])).
% 1.74/2.01 tff(7032,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[7031])).
% 1.74/2.01 tff(7033,plain,
% 1.74/2.01 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7027])).
% 1.74/2.01 tff(7034,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[7033])).
% 1.74/2.01 tff(7035,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7034, 7027])).
% 1.74/2.01 tff(7036,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[7035])).
% 1.74/2.01 tff(7037,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2654, 7028, 2520])).
% 1.74/2.01 tff(7038,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7037, 7036])).
% 1.74/2.01 tff(7039,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7038, 7032])).
% 1.74/2.01 tff(7040,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7030])).
% 1.74/2.01 tff(7041,plain,
% 1.74/2.01 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[7040])).
% 1.74/2.01 tff(7042,plain,
% 1.74/2.01 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7027, 7034])).
% 1.74/2.01 tff(7043,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[7042])).
% 1.74/2.01 tff(7044,plain,
% 1.74/2.01 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[1084, 7043])).
% 1.74/2.01 tff(7045,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7044, 7041])).
% 1.74/2.01 tff(7046,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7027])).
% 1.74/2.01 tff(7047,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[1603, 7046])).
% 1.74/2.01 tff(7048,plain,
% 1.74/2.01 ((~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(s(z)))), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6811, 337, 7047])).
% 1.74/2.01 tff(7049,plain,
% 1.74/2.01 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7048, 7045, 7039])).
% 1.74/2.01 tff(7050,plain,
% 1.74/2.01 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1539, 7049, 7029])).
% 1.74/2.01 tff(7051,plain,
% 1.74/2.01 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7033])).
% 1.74/2.01 tff(7052,plain,
% 1.74/2.01 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[1077, 7051])).
% 1.74/2.01 tff(7053,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7054,plain,
% 1.74/2.01 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7055,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7054])).
% 1.74/2.01 tff(7056,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7055, 7053])).
% 1.74/2.01 tff(7057,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7058,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)))), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7057, 7056])).
% 1.74/2.01 tff(7059,plain,
% 1.74/2.01 (~r(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7058, 189, 7052, 7050])).
% 1.74/2.01 tff(7060,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1792, 7059])).
% 1.74/2.01 tff(7061,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7062,plain,
% 1.74/2.01 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7063,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7062])).
% 1.74/2.01 tff(7064,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7063, 7061])).
% 1.74/2.01 tff(7065,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7066,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7065, 7064])).
% 1.74/2.01 tff(7067,plain,
% 1.74/2.01 (~r(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7066, 189, 7052, 7050])).
% 1.74/2.01 tff(7068,plain,
% 1.74/2.01 (b(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1786, 7067])).
% 1.74/2.01 tff(7069,plain,
% 1.74/2.01 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7027])).
% 1.74/2.01 tff(7070,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[327, 7069])).
% 1.74/2.01 tff(7071,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.01 tff(7072,plain,
% 1.74/2.01 (b(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[727, 6976, 2754])).
% 1.74/2.01 tff(7073,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1611, 7072, 1603, 1481, 274, 1591, 1592, 327])).
% 1.74/2.01 tff(7074,plain,
% 1.74/2.01 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[548, 7073])).
% 1.74/2.01 tff(7075,plain,
% 1.74/2.01 (~r(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2027, 7074, 118])).
% 1.74/2.01 tff(7076,plain,
% 1.74/2.01 (b(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1150, 7075])).
% 1.74/2.01 tff(7077,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7078,plain,
% 1.74/2.01 (((~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(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(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(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7079,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(s(s(elem!1)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7078])).
% 1.74/2.01 tff(7080,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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(s(s(elem!1))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7079, 7077])).
% 1.74/2.01 tff(7081,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7082,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7081, 7080])).
% 1.74/2.01 tff(7083,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7082, 337, 7076, 1971, 241, 7071])).
% 1.74/2.01 tff(7084,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7085,plain,
% 1.74/2.01 (~r(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7084, 7070, 7047, 118, 1603, 1481, 274, 7060, 7068, 327, 272, 215, 370])).
% 1.74/2.01 tff(7086,plain,
% 1.74/2.01 (b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[963, 7085])).
% 1.74/2.01 tff(7087,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4153, 7086, 1301, 1603, 327, 7068])).
% 1.74/2.01 tff(7088,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1150, 7087])).
% 1.74/2.01 tff(7089,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2027, 7088, 118])).
% 1.74/2.01 tff(7090,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[548, 7089])).
% 1.74/2.01 tff(7091,plain,
% 1.74/2.01 (~b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1795, 7090, 7068, 7060])).
% 1.74/2.01 tff(7092,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, 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(X1, 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(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7093,plain,
% 1.74/2.01 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7094,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~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(X1, 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(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7093])).
% 1.74/2.01 tff(7095,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~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(X1, 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(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7094, 7092])).
% 1.74/2.01 tff(7096,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7097,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7096, 7095])).
% 1.74/2.01 tff(7098,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7097, 337, 1763, 327, 791, 1, 1603, 1592])).
% 1.74/2.01 tff(7099,plain,((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7100,plain,
% 1.74/2.02 (~b(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7099, 1, 791, 327, 1603, 1592])).
% 1.74/2.02 tff(7101,plain,
% 1.74/2.02 (r(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1759, 7100, 1900])).
% 1.74/2.02 tff(7102,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1611, 7101, 791, 1603, 1481, 327, 1592, 1591])).
% 1.74/2.02 tff(7103,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[548, 7102])).
% 1.74/2.02 tff(7104,plain,
% 1.74/2.02 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1570, 337, 327, 791, 1603])).
% 1.74/2.02 tff(7105,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1150, 7104])).
% 1.74/2.02 tff(7106,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1616, 189, 7105, 7103])).
% 1.74/2.02 tff(7107,plain,
% 1.74/2.02 (b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[46, 43, 33, 7106])).
% 1.74/2.02 tff(7108,plain,
% 1.74/2.02 (~b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1633, 337, 327, 791, 7107])).
% 1.74/2.02 tff(7109,plain,
% 1.74/2.02 (r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1484, 43, 1481, 7108])).
% 1.74/2.02 tff(7110,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4209, 189, 370, 7109])).
% 1.74/2.02 tff(7111,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1312, 43, 178, 7110])).
% 1.74/2.02 tff(7112,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7113,plain,
% 1.74/2.02 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7114,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7113])).
% 1.74/2.02 tff(7115,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7114, 7112])).
% 1.74/2.02 tff(7116,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7117,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7116, 7115])).
% 1.74/2.02 tff(7118,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7117, 337, 791, 1, 1603, 1592, 7107, 7111])).
% 1.74/2.02 tff(7119,plain,((~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7120,plain,
% 1.74/2.02 (~b(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7119, 7086, 1603, 370, 68, 327, 1481, 7060, 7068])).
% 1.74/2.02 tff(7121,plain,
% 1.74/2.02 (r(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[727, 7120, 272])).
% 1.74/2.02 tff(7122,plain,
% 1.74/2.02 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[801, 7028, 247])).
% 1.74/2.02 tff(7123,plain,
% 1.74/2.02 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2760, 7122])).
% 1.74/2.02 tff(7124,plain,
% 1.74/2.02 (~b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4143, 7088, 1603, 7123, 7121, 327, 118])).
% 1.74/2.02 tff(7125,plain,
% 1.74/2.02 (r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2463, 7124, 1481])).
% 1.74/2.02 tff(7126,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4211, 7125, 370])).
% 1.74/2.02 tff(7127,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1498, 7126, 7091])).
% 1.74/2.02 tff(7128,plain,((~r(z, s(elem!1))) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7129,plain,
% 1.74/2.02 (~r(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7128, 6759, 6974, 1603, 6972, 49, 5283, 5284, 147, 6975, 247, 50, 172])).
% 1.74/2.02 tff(7130,plain,
% 1.74/2.02 (b(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[395, 7129])).
% 1.74/2.02 tff(7131,plain,
% 1.74/2.02 (~b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5659, 337, 6972, 7130, 6975, 5283, 7025])).
% 1.74/2.02 tff(7132,plain,
% 1.74/2.02 (r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1498, 7131])).
% 1.74/2.02 tff(7133,plain,
% 1.74/2.02 (~r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4211, 7132, 6759])).
% 1.74/2.02 tff(7134,plain,
% 1.74/2.02 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[801, 7018, 247])).
% 1.74/2.02 tff(7135,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7136,plain,
% 1.74/2.02 (((~b(s(z), z)) | (~b(s(z), 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), z)) | (~b(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))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7137,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7136])).
% 1.74/2.02 tff(7138,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7137, 7135])).
% 1.74/2.02 tff(7139,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), 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))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7140,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7139, 7138])).
% 1.74/2.02 tff(7141,plain,
% 1.74/2.02 ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7140, 337, 327, 1, 1603])).
% 1.74/2.02 tff(7142,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7141, 791])).
% 1.74/2.02 tff(7143,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[851, 7142])).
% 1.74/2.02 tff(7144,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7145,plain,
% 1.74/2.02 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7146,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7145])).
% 1.74/2.02 tff(7147,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7146, 7144])).
% 1.74/2.02 tff(7148,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7149,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7148, 7147])).
% 1.74/2.02 tff(7150,plain,
% 1.74/2.02 ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7149, 337, 327, 2520, 1])).
% 1.74/2.02 tff(7151,plain,
% 1.74/2.02 (~b(s(elem!1), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7150, 791])).
% 1.74/2.02 tff(7152,plain,
% 1.74/2.02 (r(s(elem!1), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[898, 7151, 50])).
% 1.74/2.02 tff(7153,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[827, 189, 7152, 7143])).
% 1.74/2.02 tff(7154,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6989, 337, 327, 2520, 791, 1603])).
% 1.74/2.02 tff(7155,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[832, 43, 829, 7154, 7153])).
% 1.74/2.02 tff(7156,plain,((~b(s(z), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7157,plain,
% 1.74/2.02 (~b(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7156, 6973, 6972, 6975, 1603, 50, 6994])).
% 1.74/2.02 tff(7158,plain,
% 1.74/2.02 (r(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[727, 7157, 272])).
% 1.74/2.02 tff(7159,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4143, 1735, 4102, 327, 4121, 2454, 118])).
% 1.74/2.02 tff(7160,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1150, 7159])).
% 1.74/2.02 tff(7161,plain,
% 1.74/2.02 (~b(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4153, 7160, 1, 1301, 4121, 327])).
% 1.74/2.02 tff(7162,plain,
% 1.74/2.02 (r(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1786, 7161])).
% 1.74/2.02 tff(7163,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5075, 7162, 1474])).
% 1.74/2.02 tff(7164,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[548, 7163])).
% 1.74/2.02 tff(7165,plain,
% 1.74/2.02 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4133, 337, 327, 7164, 4121, 2454])).
% 1.74/2.02 tff(7166,plain,
% 1.74/2.02 (r(elem!1, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2845, 43, 4102, 7165])).
% 1.74/2.02 tff(7167,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4162, 189, 274, 7162, 7166])).
% 1.74/2.02 tff(7168,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7169,plain,
% 1.74/2.02 (~b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7168, 7132, 5284, 6972, 7158, 6994, 5283, 49, 7134, 6759])).
% 1.74/2.02 tff(7170,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2463, 7169, 7133, 6974])).
% 1.86/2.02 tff(7171,plain,((elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(z))), s(z)) | b(z, s(s(s(elem!1)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(7172,plain,
% 1.86/2.02 (elem!1 = s(z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[7171, 4858, 50, 1603, 3, 82, 172])).
% 1.86/2.02 tff(7173,plain,
% 1.86/2.02 (s(elem!1) = s(s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7172])).
% 1.86/2.02 tff(7174,plain,
% 1.86/2.02 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7173])).
% 1.86/2.02 tff(7175,plain,
% 1.86/2.02 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7172])).
% 1.86/2.02 tff(7176,plain,
% 1.86/2.02 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.86/2.02 inference(transitivity,[status(thm)],[7175, 7174])).
% 1.86/2.02 tff(7177,plain,
% 1.86/2.02 (r(elem!1, z) <=> r(s(z), z)),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7172])).
% 1.86/2.02 tff(7178,plain,
% 1.86/2.02 (r(s(z), z)),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[5284, 7177])).
% 1.86/2.02 tff(7179,plain,
% 1.86/2.02 (~r(s(elem!1), elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1699, 7178, 82, 172, 50, 5284])).
% 1.86/2.02 tff(7180,plain,
% 1.86/2.02 (b(s(elem!1), elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[270, 7179, 265])).
% 1.86/2.02 tff(7181,plain,
% 1.86/2.02 (b(s(s(z)), s(z))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[7180, 7176])).
% 1.86/2.02 tff(7182,plain,
% 1.86/2.02 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7173])).
% 1.86/2.02 tff(7183,plain,
% 1.86/2.02 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7172])).
% 1.86/2.02 tff(7184,plain,
% 1.86/2.02 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[1603, 7183])).
% 1.86/2.02 tff(7185,plain,
% 1.86/2.02 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1144, 7172, 5679])).
% 1.86/2.02 tff(7186,plain,
% 1.86/2.02 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1150, 7185])).
% 1.86/2.02 tff(7187,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7188,plain,
% 1.86/2.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(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(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7189,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(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(X1, 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(s(s(s(z)))), s(z)))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7188])).
% 1.86/2.02 tff(7190,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(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(X1, 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(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[7189, 7187])).
% 1.86/2.02 tff(7191,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(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)))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(7192,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[7191, 7190])).
% 1.86/2.02 tff(7193,plain,
% 1.86/2.02 (~b(s(s(s(s(z)))), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[7192, 337, 5283, 7186, 7184])).
% 1.86/2.02 tff(7194,plain,
% 1.86/2.02 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7172])).
% 1.86/2.02 tff(7195,plain,
% 1.86/2.02 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.02 inference(symmetry,[status(thm)],[7194])).
% 1.86/2.02 tff(7196,plain,
% 1.86/2.02 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7173])).
% 1.86/2.02 tff(7197,plain,
% 1.86/2.02 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7196])).
% 1.86/2.02 tff(7198,plain,
% 1.86/2.02 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7197])).
% 1.86/2.02 tff(7199,plain,
% 1.86/2.02 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.02 inference(symmetry,[status(thm)],[7198])).
% 1.86/2.02 tff(7200,plain,
% 1.86/2.02 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.02 inference(transitivity,[status(thm)],[7199, 7195])).
% 1.86/2.02 tff(7201,plain,
% 1.86/2.02 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[7184, 7200])).
% 1.86/2.02 tff(7202,plain,
% 1.86/2.02 (b(z, s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[3170, 7179, 5284, 172, 7172, 7201, 7193])).
% 1.86/2.02 tff(7203,plain,
% 1.86/2.02 (b(z, s(s(z)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[7202, 7182])).
% 1.86/2.02 tff(7204,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7205,plain,
% 1.86/2.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), 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(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7206,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7205])).
% 1.86/2.02 tff(7207,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[7206, 7204])).
% 1.86/2.02 tff(7208,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7209,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7208, 7207])).
% 1.86/2.03 tff(7210,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7209, 337, 5283, 7186, 7184, 7203, 7181])).
% 1.86/2.03 tff(7211,plain,(b(elem!1, z) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7212,plain,
% 1.86/2.03 (b(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7211, 172, 82, 50, 1603, 3])).
% 1.86/2.03 tff(7213,plain,
% 1.86/2.03 (~r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6204, 273, 3844, 50, 1763, 247])).
% 1.86/2.03 tff(7214,plain,
% 1.86/2.03 (b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[921, 7213, 61])).
% 1.86/2.03 tff(7215,plain,
% 1.86/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[928, 7214, 82])).
% 1.86/2.03 tff(7216,plain,
% 1.86/2.03 (b(elem!1, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6533, 7214, 1763, 247, 7215, 147, 118, 3844, 172, 50])).
% 1.86/2.03 tff(7217,plain,
% 1.86/2.03 (~b(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4005, 7214, 3844, 1763])).
% 1.86/2.03 tff(7218,plain,
% 1.86/2.03 (r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[727, 7217, 272])).
% 1.86/2.03 tff(7219,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4077, 7218, 7216, 273, 3844, 7214, 50])).
% 1.86/2.03 tff(7220,plain,((~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7221,plain,
% 1.86/2.03 (~r(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7220, 247, 1763, 50, 118, 172, 82])).
% 1.86/2.03 tff(7222,plain,
% 1.86/2.03 (b(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[270, 7221, 265])).
% 1.86/2.03 tff(7223,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6533, 1712, 925, 1763, 247, 4370, 147, 118, 3844, 172, 50])).
% 1.86/2.03 tff(7224,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | b(elem!1, s(z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7225,plain,
% 1.86/2.03 (~b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7224, 4370, 247, 1763, 118, 172, 50, 82])).
% 1.86/2.03 tff(7226,plain,
% 1.86/2.03 (r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[921, 7225, 61])).
% 1.86/2.03 tff(7227,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[752, 189, 370, 352, 215])).
% 1.86/2.03 tff(7228,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7229,plain,
% 1.86/2.03 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7228, 7226, 147])).
% 1.86/2.03 tff(7230,plain,
% 1.86/2.03 (~r(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6317, 788, 777])).
% 1.86/2.03 tff(7231,plain,
% 1.86/2.03 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3157, 7230, 3062, 365, 978])).
% 1.86/2.03 tff(7232,plain,
% 1.86/2.03 (s(s(s(elem!1))) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[350, 7231, 1899])).
% 1.86/2.03 tff(7233,plain,
% 1.86/2.03 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7232])).
% 1.86/2.03 tff(7234,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7233])).
% 1.86/2.03 tff(7235,plain,
% 1.86/2.03 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7234])).
% 1.86/2.03 tff(7236,plain,
% 1.86/2.03 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7235])).
% 1.86/2.03 tff(7237,plain,
% 1.86/2.03 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7232])).
% 1.86/2.03 tff(7238,plain,
% 1.86/2.03 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7237])).
% 1.86/2.03 tff(7239,plain,
% 1.86/2.03 (~(s(s(s(z))) = elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2470, 7238])).
% 1.86/2.03 tff(7240,plain,
% 1.86/2.03 (b(s(s(s(z))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2463, 7239, 4938])).
% 1.86/2.03 tff(7241,plain,
% 1.86/2.03 (b(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1015, 7230, 3146])).
% 1.86/2.03 tff(7242,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5868, 337, 3948, 7241, 7240])).
% 1.86/2.03 tff(7243,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7242, 7236])).
% 1.86/2.03 tff(7244,plain,
% 1.86/2.03 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7233])).
% 1.86/2.03 tff(7245,plain,
% 1.86/2.03 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7244])).
% 1.86/2.03 tff(7246,plain,
% 1.86/2.03 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7245])).
% 1.86/2.03 tff(7247,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5616, 7246])).
% 1.86/2.03 tff(7248,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1821, 7247])).
% 1.86/2.03 tff(7249,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7248, 7243])).
% 1.86/2.03 tff(7250,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | r(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7251,plain,
% 1.86/2.03 (~r(s(elem!1), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7250, 1084, 2451, 1899, 3062, 118, 265, 777])).
% 1.86/2.03 tff(7252,plain,
% 1.86/2.03 (b(s(elem!1), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[898, 7251, 50])).
% 1.86/2.03 tff(7253,plain,
% 1.86/2.03 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6243, 7252, 1301, 1763, 3079, 1084])).
% 1.86/2.03 tff(7254,plain,
% 1.86/2.03 (s(s(s(elem!1))) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[350, 7253, 1899])).
% 1.86/2.03 tff(7255,plain,
% 1.86/2.03 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7254])).
% 1.86/2.03 tff(7256,plain,
% 1.86/2.03 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7255])).
% 1.86/2.03 tff(7257,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7256])).
% 1.86/2.03 tff(7258,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7257])).
% 1.86/2.03 tff(7259,plain,
% 1.86/2.03 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7258])).
% 1.86/2.03 tff(7260,plain,
% 1.86/2.03 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1466, 7254, 50])).
% 1.86/2.03 tff(7261,plain,
% 1.86/2.03 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 1.86/2.03 tff(7262,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7263,plain,
% 1.86/2.03 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7264,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7263])).
% 1.86/2.03 tff(7265,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7264, 7262])).
% 1.86/2.03 tff(7266,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7267,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7266, 7265])).
% 1.86/2.03 tff(7268,plain,
% 1.86/2.03 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7267, 337, 1763, 2520, 1544, 1301, 1603])).
% 1.86/2.03 tff(7269,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[832, 43, 829, 7268])).
% 1.86/2.03 tff(7270,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2966, 189, 1077, 7269])).
% 1.86/2.03 tff(7271,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[820, 43, 817, 7270])).
% 1.86/2.03 tff(7272,plain,
% 1.86/2.03 (~r(z, s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4698, 189, 1077, 7269])).
% 1.86/2.03 tff(7273,plain,
% 1.86/2.03 (b(z, s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1584, 43, 7272, 1562])).
% 1.86/2.03 tff(7274,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1908, 7273, 7271, 1763, 1603])).
% 1.86/2.03 tff(7275,plain,((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7276,plain,
% 1.86/2.03 (s(s(s(s(z)))) = s(elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7275, 7252, 1301, 1603, 1763, 3079, 1077])).
% 1.86/2.03 tff(7277,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7276, 7261])).
% 1.86/2.03 tff(7278,plain,((~r(z, s(elem!1))) | (s(elem!1) = s(z)) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | r(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7279,plain,
% 1.86/2.03 (~r(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7278, 7229, 50, 3844, 1763, 1603, 7221, 118, 5940, 172, 147])).
% 1.86/2.03 tff(7280,plain,
% 1.86/2.03 (b(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[395, 7279])).
% 1.86/2.03 tff(7281,plain,
% 1.86/2.03 (~b(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6311, 7280, 1763, 7222])).
% 1.86/2.03 tff(7282,plain,
% 1.86/2.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1082, 1077, 147])).
% 1.86/2.03 tff(7283,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[363, 7282, 172])).
% 1.86/2.03 tff(7284,plain,
% 1.86/2.03 (~r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6267, 7283, 2520, 1301, 147, 1763, 5308, 981, 1077, 2754, 275])).
% 1.86/2.03 tff(7285,plain,
% 1.86/2.03 (b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[921, 7284, 65])).
% 1.86/2.03 tff(7286,plain,
% 1.86/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[928, 7285, 82])).
% 1.86/2.03 tff(7287,plain,
% 1.86/2.03 (~b(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4005, 7285, 1301, 1763])).
% 1.86/2.03 tff(7288,plain,
% 1.86/2.03 (~b(s(elem!1), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3977, 7285])).
% 1.86/2.03 tff(7289,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5047, 7288, 7287, 4370, 6209, 3062, 147, 1077, 7286])).
% 1.86/2.03 tff(7290,plain,((~r(z, s(elem!1))) | b(elem!1, s(z)) | r(s(elem!1), elem!1) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | b(z, s(s(s(elem!1)))) | (z = elem!1) | (s(z) = elem!1) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7291,plain,
% 1.86/2.03 (~r(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7290, 275, 1301, 1763, 2754, 3062, 82, 61, 4370, 3079, 172])).
% 1.86/2.03 tff(7292,plain,
% 1.86/2.03 (b(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[395, 7291])).
% 1.86/2.03 tff(7293,plain,
% 1.86/2.03 (~b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2717, 7292, 1763, 3079])).
% 1.86/2.03 tff(7294,plain,
% 1.86/2.03 (r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[921, 7293, 61])).
% 1.86/2.03 tff(7295,plain,
% 1.86/2.03 (~r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3855, 7294, 275])).
% 1.86/2.03 tff(7296,plain,
% 1.86/2.03 (b(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[727, 7295, 2754])).
% 1.86/2.03 tff(7297,plain,
% 1.86/2.03 (~b(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6311, 7292, 1763, 3079])).
% 1.86/2.03 tff(7298,plain,
% 1.86/2.03 (r(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1015, 7297, 981])).
% 1.86/2.03 tff(7299,plain,
% 1.86/2.03 (~r(s(elem!1), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6317, 7298, 777])).
% 1.86/2.03 tff(7300,plain,
% 1.86/2.03 (b(s(elem!1), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[898, 7299, 50])).
% 1.86/2.03 tff(7301,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7302,plain,
% 1.86/2.03 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7303,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7302])).
% 1.86/2.03 tff(7304,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7303, 7301])).
% 1.86/2.03 tff(7305,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7306,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7305, 7304])).
% 1.86/2.03 tff(7307,plain,
% 1.86/2.03 (~b(s(z), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7306, 337, 7292, 7300, 7296, 1301])).
% 1.86/2.03 tff(7308,plain,
% 1.86/2.03 (r(s(z), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2133, 43, 7307, 55])).
% 1.86/2.03 tff(7309,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5375, 189, 7298, 777, 7308])).
% 1.86/2.03 tff(7310,plain,((~r(s(z), z)) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~b(elem!1, z)) | r(s(elem!1), elem!1) | b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7311,plain,
% 1.86/2.03 (~r(s(z), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7310, 5940, 3844, 50, 272, 1763, 7221, 82, 4370, 172])).
% 1.86/2.03 tff(7312,plain,
% 1.86/2.03 (b(s(z), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[963, 7311])).
% 1.86/2.03 tff(7313,plain,
% 1.86/2.03 (~r(elem!1, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6321, 7280, 3844, 50, 1763, 247, 7312])).
% 1.86/2.03 tff(7314,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1015, 7313, 7281, 981])).
% 1.86/2.03 tff(7315,plain,(b(elem!1, s(z)) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7316,plain,
% 1.86/2.03 (b(elem!1, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7315, 247, 7212, 50, 1603, 49, 172, 82])).
% 1.86/2.03 tff(7317,plain,
% 1.86/2.03 (~b(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3908, 7316, 5283, 7212])).
% 1.86/2.03 tff(7318,plain,
% 1.86/2.03 (r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[727, 7317, 272])).
% 1.86/2.03 tff(7319,plain,
% 1.86/2.03 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5572, 7316, 3])).
% 1.86/2.03 tff(7320,plain,
% 1.86/2.03 (~r(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7220, 247, 7212, 50, 49, 172, 82])).
% 1.86/2.03 tff(7321,plain,
% 1.86/2.03 (b(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[270, 7320, 265])).
% 1.86/2.03 tff(7322,plain,
% 1.86/2.03 (~b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3995, 7321, 7212, 5283, 1603, 7319])).
% 1.86/2.03 tff(7323,plain,
% 1.86/2.03 (r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[921, 7322, 61])).
% 1.86/2.03 tff(7324,plain,
% 1.86/2.03 (~r(s(z), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3855, 7323, 7318])).
% 1.86/2.03 tff(7325,plain,
% 1.86/2.03 (b(s(z), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[963, 7324])).
% 1.86/2.03 tff(7326,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4097, 337, 7212, 7316, 7325, 5283])).
% 1.86/2.03 tff(7327,plain,((elem!1 = s(z)) | (~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7328,plain,
% 1.86/2.03 (elem!1 = s(z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7327, 6757, 3, 50, 172, 82])).
% 1.86/2.03 tff(7329,plain,
% 1.86/2.03 (s(elem!1) = s(s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7328])).
% 1.86/2.03 tff(7330,plain,
% 1.86/2.03 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7329])).
% 1.86/2.03 tff(7331,plain,
% 1.86/2.03 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7328])).
% 1.86/2.03 tff(7332,plain,
% 1.86/2.03 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7331, 7330])).
% 1.86/2.03 tff(7333,plain,
% 1.86/2.03 (b(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6585, 7328, 5283])).
% 1.86/2.03 tff(7334,plain,
% 1.86/2.03 (b(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7211, 172, 82, 50, 6757, 3])).
% 1.86/2.03 tff(7335,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.03 inference(commutativity,[status(thm)],[])).
% 1.86/2.03 tff(7336,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7329])).
% 1.86/2.03 tff(7337,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7336, 7335])).
% 1.86/2.03 tff(7338,plain,
% 1.86/2.03 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7337])).
% 1.86/2.03 tff(7339,plain,
% 1.86/2.03 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7338])).
% 1.86/2.03 tff(7340,plain,
% 1.86/2.03 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2263, 7339])).
% 1.86/2.03 tff(7341,plain,
% 1.86/2.03 (~b(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3995, 7340, 7334, 5283, 6757, 7333])).
% 1.86/2.03 tff(7342,plain,
% 1.86/2.03 (r(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[270, 7341, 265])).
% 1.86/2.03 tff(7343,plain,
% 1.86/2.03 (r(s(s(z)), s(z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7342, 7332])).
% 1.86/2.03 tff(7344,plain,
% 1.86/2.03 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1293, 189, 49, 7343])).
% 1.86/2.03 tff(7345,plain,
% 1.86/2.03 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4268, 7344])).
% 1.86/2.03 tff(7346,plain,
% 1.86/2.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7347,plain,
% 1.86/2.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7348,plain,
% 1.86/2.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7347, 7346])).
% 1.86/2.03 tff(7349,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7348, 189, 49, 7343])).
% 1.86/2.03 tff(7350,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2854, 7349])).
% 1.86/2.03 tff(7351,plain,
% 1.86/2.03 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7329])).
% 1.86/2.03 tff(7352,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7328])).
% 1.86/2.03 tff(7353,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6757, 7352])).
% 1.86/2.03 tff(7354,plain,
% 1.86/2.03 (b(s(z), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6686, 7328, 7334])).
% 1.86/2.03 tff(7355,plain,
% 1.86/2.03 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.03 inference(commutativity,[status(thm)],[])).
% 1.86/2.03 tff(7356,plain,
% 1.86/2.03 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7329])).
% 1.86/2.03 tff(7357,plain,
% 1.86/2.03 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7356])).
% 1.86/2.03 tff(7358,plain,
% 1.86/2.03 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7357])).
% 1.86/2.03 tff(7359,plain,
% 1.86/2.03 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7358, 7329])).
% 1.86/2.03 tff(7360,plain,
% 1.86/2.03 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7359, 7355])).
% 1.86/2.03 tff(7361,plain,
% 1.86/2.03 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7360])).
% 1.86/2.03 tff(7362,plain,
% 1.86/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[928, 7333, 82])).
% 1.86/2.03 tff(7363,plain,
% 1.86/2.03 (~(elem!1 = s(s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[281, 7362])).
% 1.86/2.03 tff(7364,plain,
% 1.86/2.03 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[632, 7363])).
% 1.86/2.03 tff(7365,plain,
% 1.86/2.03 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7364, 7361])).
% 1.86/2.03 tff(7366,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7367,plain,
% 1.86/2.03 (((~b(z, s(z))) | (~b(z, s(z))) | (~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(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7368,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7367])).
% 1.86/2.03 tff(7369,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7368, 7366])).
% 1.86/2.03 tff(7370,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7371,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7370, 7369])).
% 1.86/2.03 tff(7372,plain,
% 1.86/2.03 ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7371, 337, 7334, 5283, 6757])).
% 1.86/2.03 tff(7373,plain,
% 1.86/2.03 (~b(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7372, 7333])).
% 1.86/2.03 tff(7374,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1792, 7373])).
% 1.86/2.03 tff(7375,plain,
% 1.86/2.03 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[231])).
% 1.86/2.03 tff(7376,plain,
% 1.86/2.03 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.86/2.03 inference(transitivity,[status(thm)],[1188, 7375])).
% 1.86/2.03 tff(7377,plain,
% 1.86/2.03 (r(s(s(z)), s(z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[273, 7376])).
% 1.86/2.03 tff(7378,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7348, 189, 118, 7377])).
% 1.86/2.03 tff(7379,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2854, 7378])).
% 1.86/2.03 tff(7380,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[1084, 1182])).
% 1.86/2.03 tff(7381,plain,
% 1.86/2.03 (r(z, s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1108, 1077, 230])).
% 1.86/2.03 tff(7382,plain,
% 1.86/2.03 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1125, 7381, 230, 3048])).
% 1.86/2.04 tff(7383,plain,
% 1.86/2.04 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[579, 7382, 428])).
% 1.86/2.04 tff(7384,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1133, 7383, 230])).
% 1.86/2.04 tff(7385,assumption,(~(s(s(z)) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.04 tff(7386,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1293, 189, 118, 7377])).
% 1.86/2.04 tff(7387,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4268, 7386])).
% 1.86/2.04 tff(7388,plain,
% 1.86/2.04 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.86/2.04 inference(symmetry,[status(thm)],[3111])).
% 1.86/2.04 tff(7389,plain,
% 1.86/2.04 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[231])).
% 1.86/2.04 tff(7390,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[7389])).
% 1.86/2.04 tff(7391,plain,
% 1.86/2.04 (b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[1396, 7390])).
% 1.86/2.04 tff(7392,plain,
% 1.86/2.04 (r(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1874, 273, 230])).
% 1.86/2.04 tff(7393,plain,
% 1.86/2.04 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[231])).
% 1.86/2.04 tff(7394,plain,
% 1.86/2.04 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = s(elem!1))),
% 1.86/2.04 inference(symmetry,[status(thm)],[7393])).
% 1.86/2.04 tff(7395,plain,
% 1.86/2.04 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7394])).
% 1.86/2.04 tff(7396,plain,
% 1.86/2.04 (~(s(s(s(z))) = s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2009, 7395])).
% 1.86/2.04 tff(7397,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4847, 1275, 1231, 7396, 1, 7392, 7391])).
% 1.86/2.04 tff(7398,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[548, 7397])).
% 1.86/2.04 tff(7399,plain,
% 1.86/2.04 (~r(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5118, 189, 7398, 1115])).
% 1.86/2.04 tff(7400,plain,
% 1.86/2.04 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[199, 43, 7399])).
% 1.86/2.04 tff(7401,plain,
% 1.86/2.04 (b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7400, 179])).
% 1.86/2.04 tff(7402,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[3107])).
% 1.86/2.04 tff(7403,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.86/2.04 tff(7404,plain,
% 1.86/2.04 (~r(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5075, 7398, 1115])).
% 1.86/2.04 tff(7405,plain,
% 1.86/2.04 (b(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1498, 7404])).
% 1.86/2.04 tff(7406,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7407,plain,
% 1.86/2.04 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7408,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7407])).
% 1.86/2.04 tff(7409,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7408, 7406])).
% 1.86/2.04 tff(7410,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), 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)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7411,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7410, 7409])).
% 1.86/2.04 tff(7412,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7411, 337, 1301, 1231, 1396, 7405, 7403])).
% 1.86/2.04 tff(7413,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[524, 7412])).
% 1.86/2.04 tff(7414,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7415,plain,
% 1.86/2.04 (((~b(s(z), z)) | (~b(s(s(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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7416,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(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(X1, 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), s(s(s(z)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7415])).
% 1.86/2.04 tff(7417,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(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(X1, 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), s(s(s(z))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7416, 7414])).
% 1.86/2.04 tff(7418,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7419,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 1.86/2.04 tff(7420,plain,
% 1.86/2.04 (~b(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7419, 337, 1, 1301, 7405])).
% 1.86/2.04 tff(7421,plain,
% 1.86/2.04 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2796, 43, 7420])).
% 1.86/2.04 tff(7422,plain,
% 1.86/2.04 (r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7421, 2781])).
% 1.86/2.04 tff(7423,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6502, 7422, 1, 1231, 3466, 1275, 7413])).
% 1.86/2.04 tff(7424,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3252, 7423])).
% 1.86/2.04 tff(7425,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7424, 7402])).
% 1.86/2.04 tff(7426,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7427,plain,
% 1.86/2.04 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7428,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7427])).
% 1.86/2.04 tff(7429,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7428, 7426])).
% 1.86/2.04 tff(7430,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7431,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7430, 7429])).
% 1.86/2.04 tff(7432,plain,
% 1.86/2.04 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7431, 337, 1301, 7405, 7425, 7401])).
% 1.86/2.04 tff(7433,plain,
% 1.86/2.04 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7432, 3504])).
% 1.86/2.04 tff(7434,plain,
% 1.86/2.04 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[663, 7433])).
% 1.86/2.04 tff(7435,plain,
% 1.86/2.04 (r(s(s(s(s(s(z))))), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7434, 7388])).
% 1.86/2.04 tff(7436,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.04 tff(7437,plain,
% 1.86/2.04 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[230, 3107])).
% 1.86/2.04 tff(7438,plain,
% 1.86/2.04 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6674])).
% 1.86/2.04 tff(7439,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[135, 7438])).
% 1.86/2.04 tff(7440,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7441,plain,
% 1.86/2.04 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(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(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7442,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7441])).
% 1.86/2.04 tff(7443,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7442, 7440])).
% 1.86/2.04 tff(7444,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(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(s(z))))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7445,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7444, 7443])).
% 1.86/2.04 tff(7446,plain,
% 1.86/2.04 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7445, 337, 7405, 7403, 7425, 7401])).
% 1.86/2.04 tff(7447,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3299, 7446, 7385])).
% 1.86/2.04 tff(7448,plain,
% 1.86/2.04 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[617])).
% 1.86/2.04 tff(7449,plain,
% 1.86/2.04 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[454, 7448])).
% 1.86/2.04 tff(7450,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[7449])).
% 1.86/2.04 tff(7451,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.04 tff(7452,plain,
% 1.86/2.04 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7451, 7450])).
% 1.86/2.04 tff(7453,plain,
% 1.86/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7454,plain,
% 1.86/2.04 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7455,plain,
% 1.86/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7454])).
% 1.86/2.04 tff(7456,plain,
% 1.86/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7455, 7453])).
% 1.86/2.04 tff(7457,plain,
% 1.86/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7458,plain,
% 1.86/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7457, 7456])).
% 1.86/2.04 tff(7459,plain,
% 1.86/2.04 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7458, 189, 3277, 273])).
% 1.86/2.04 tff(7460,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7459, 7452])).
% 1.86/2.04 tff(7461,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(7462,plain,
% 1.86/2.04 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7461, 7447, 1273, 273])).
% 1.86/2.04 tff(7463,plain,
% 1.86/2.04 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3274, 7462, 7439])).
% 1.86/2.04 tff(7464,plain,
% 1.86/2.04 (b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7463, 7437])).
% 1.86/2.04 tff(7465,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.86/2.04 tff(7466,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(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(X1, 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(s(s(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(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7467,plain,
% 1.86/2.05 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)))))))) <=> ((~b(s(z), s(s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7468,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7467])).
% 1.86/2.05 tff(7469,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7468, 7466])).
% 1.86/2.05 tff(7470,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7471,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7470, 7469])).
% 1.86/2.05 tff(7472,plain,
% 1.86/2.05 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7471, 337, 1275, 7465, 7403, 7425])).
% 1.86/2.05 tff(7473,plain,
% 1.86/2.05 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7472, 7464])).
% 1.86/2.05 tff(7474,plain,
% 1.86/2.05 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6726, 7473, 7436])).
% 1.86/2.05 tff(7475,plain,
% 1.86/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7476,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7477,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7476, 7475])).
% 1.86/2.05 tff(7478,plain,
% 1.86/2.05 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7477, 189, 1168, 7474])).
% 1.86/2.05 tff(7479,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7478, 7435])).
% 1.86/2.05 tff(7480,plain,((~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (s(s(z)) = s(s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7481,plain,
% 1.86/2.05 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7480, 7380, 1168, 6717, 230, 7387, 273, 7385, 1301, 1, 1231, 3130, 7384, 3048])).
% 1.86/2.05 tff(7482,plain,
% 1.86/2.05 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1150, 7481])).
% 1.86/2.05 tff(7483,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2027, 7482, 118])).
% 1.86/2.05 tff(7484,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[548, 7483])).
% 1.86/2.05 tff(7485,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7486,plain,
% 1.86/2.05 (((~b(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(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(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(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7487,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~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(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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7486])).
% 1.86/2.05 tff(7488,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~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(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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7487, 7485])).
% 1.86/2.05 tff(7489,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~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(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7490,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 1.86/2.05 tff(7491,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7490, 337, 7484, 7384, 7380, 7379])).
% 1.86/2.05 tff(7492,plain,((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~r(s(elem!1), elem!1)) | (s(s(z)) = s(s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7493,plain,
% 1.86/2.05 (~r(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7492, 7374, 49, 7328, 7342, 7365, 5283, 7354, 7353, 172, 147])).
% 1.86/2.05 tff(7494,plain,
% 1.86/2.05 (b(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[395, 7493])).
% 1.86/2.05 tff(7495,plain,
% 1.86/2.05 (b(z, s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7494, 7351])).
% 1.86/2.05 tff(7496,plain,
% 1.86/2.05 (r(z, s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3047, 7328, 147])).
% 1.86/2.05 tff(7497,plain,
% 1.86/2.05 (~r(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5075, 1339, 1115])).
% 1.86/2.05 tff(7498,plain,
% 1.86/2.05 (b(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1498, 7497])).
% 1.86/2.05 tff(7499,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7500,plain,
% 1.86/2.05 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7501,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7500])).
% 1.86/2.05 tff(7502,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7501, 7499])).
% 1.86/2.05 tff(7503,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7504,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7503, 7502])).
% 1.86/2.05 tff(7505,plain,
% 1.86/2.05 (~b(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7504, 337, 1342, 7498, 2856, 7403])).
% 1.86/2.05 tff(7506,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5120, 7505, 179])).
% 1.86/2.05 tff(7507,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7508,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7507, 7495, 7350, 7345, 7496])).
% 1.86/2.05 tff(7509,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[548, 7508])).
% 1.86/2.05 tff(7510,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7511,plain,
% 1.86/2.05 (((~b(s(s(s(z))), s(s(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(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7512,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7511])).
% 1.86/2.05 tff(7513,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7512, 7510])).
% 1.86/2.05 tff(7514,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7515,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7514, 7513])).
% 1.86/2.05 tff(7516,plain,
% 1.86/2.05 (~b(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7515, 337, 7509, 7495, 7350, 7345])).
% 1.86/2.05 tff(7517,plain,
% 1.86/2.05 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[199, 43, 7516])).
% 1.86/2.05 tff(7518,plain,
% 1.86/2.05 (r(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7517, 179])).
% 1.86/2.05 tff(7519,plain,
% 1.86/2.05 (r(s(elem!1), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1874, 7342, 7328])).
% 1.86/2.05 tff(7520,plain,
% 1.86/2.05 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7357])).
% 1.86/2.05 tff(7521,plain,
% 1.86/2.05 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7520])).
% 1.86/2.05 tff(7522,plain,
% 1.86/2.05 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7358])).
% 1.86/2.05 tff(7523,plain,
% 1.86/2.05 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7522])).
% 1.86/2.05 tff(7524,plain,
% 1.86/2.05 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7523, 681])).
% 1.86/2.05 tff(7525,plain,
% 1.86/2.05 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7524])).
% 1.86/2.05 tff(7526,plain,
% 1.86/2.05 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7525])).
% 1.86/2.05 tff(7527,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7357])).
% 1.86/2.05 tff(7528,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7527, 681])).
% 1.86/2.05 tff(7529,plain,
% 1.86/2.05 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7528])).
% 1.86/2.05 tff(7530,plain,
% 1.86/2.05 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3129, 7529])).
% 1.86/2.05 tff(7531,plain,
% 1.86/2.05 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7530, 7526])).
% 1.86/2.05 tff(7532,plain,
% 1.86/2.05 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4847, 1275, 1231, 7396, 1, 7392, 2])).
% 1.86/2.05 tff(7533,plain,
% 1.86/2.05 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7389])).
% 1.86/2.05 tff(7534,assumption,(~b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.05 tff(7535,plain,
% 1.86/2.05 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7534, 7533])).
% 1.86/2.05 tff(7536,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1396, 7535])).
% 1.86/2.05 tff(7537,plain,((~b(s(s(z)), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7538,plain,
% 1.86/2.05 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7537, 7532, 230])).
% 1.86/2.05 tff(7539,plain,
% 1.86/2.05 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2268, 7538])).
% 1.86/2.05 tff(7540,plain,
% 1.86/2.05 (~r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4338, 189, 1115, 7539])).
% 1.86/2.05 tff(7541,plain,
% 1.86/2.05 (b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2242, 7540])).
% 1.86/2.05 tff(7542,plain,
% 1.86/2.05 (~b(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1307, 337, 1301, 1275, 2, 7541, 7403])).
% 1.86/2.05 tff(7543,plain,
% 1.86/2.05 (r(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1498, 7542])).
% 1.86/2.05 tff(7544,assumption,(~(s(s(s(s(s(z))))) = s(s(s(z))))), introduced(assumption)).
% 1.86/2.05 tff(7545,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.86/2.05 tff(7546,plain,
% 1.86/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7547,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7548,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7547, 7546])).
% 1.86/2.05 tff(7549,plain,
% 1.86/2.05 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7548, 189, 1474])).
% 1.86/2.05 tff(7550,plain,
% 1.86/2.05 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7549, 7545])).
% 1.86/2.05 tff(7551,plain,
% 1.86/2.05 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6709, 7550, 7544])).
% 1.86/2.05 tff(7552,plain,
% 1.86/2.05 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7477, 189, 1168])).
% 1.86/2.05 tff(7553,plain,
% 1.86/2.05 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7552, 7545])).
% 1.86/2.05 tff(7554,plain,
% 1.86/2.05 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6726, 7553, 7436])).
% 1.86/2.05 tff(7555,plain,
% 1.86/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7556,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7557,plain,
% 1.86/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7556, 7555])).
% 1.86/2.05 tff(7558,plain,
% 1.86/2.05 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7557, 189, 1474, 1168])).
% 1.86/2.05 tff(7559,plain,
% 1.86/2.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[524, 7558])).
% 1.86/2.05 tff(7560,plain,
% 1.86/2.05 (((~b(s(s(s(s(z)))), 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(s(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(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7561,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7560])).
% 1.86/2.05 tff(7562,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7561, 3244])).
% 1.86/2.05 tff(7563,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7564,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7563, 7562])).
% 1.86/2.06 tff(7565,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7564, 337, 7559, 2, 7554, 7551])).
% 1.86/2.06 tff(7566,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7567,plain,
% 1.86/2.06 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7566, 7543, 7436, 6667, 1168, 2])).
% 1.86/2.06 tff(7568,plain,
% 1.86/2.06 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7567, 3112])).
% 1.86/2.06 tff(7569,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[663, 7568])).
% 1.86/2.06 tff(7570,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7569, 3110])).
% 1.86/2.06 tff(7571,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[598, 3110])).
% 1.86/2.06 tff(7572,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.06 tff(7573,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7574,plain,
% 1.86/2.06 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7575,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7574])).
% 1.86/2.06 tff(7576,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7575, 7573])).
% 1.86/2.06 tff(7577,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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))))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7578,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7577, 7576])).
% 1.86/2.06 tff(7579,plain,
% 1.86/2.06 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7578, 337, 1, 1301, 7572, 1274])).
% 1.86/2.06 tff(7580,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7579, 7571])).
% 1.86/2.06 tff(7581,plain,((~b(s(s(s(s(elem!1)))), z)) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7582,plain,
% 1.86/2.06 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7581, 7569, 1, 1301, 230, 7541])).
% 1.86/2.06 tff(7583,plain,
% 1.86/2.06 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3299, 7582, 7385])).
% 1.86/2.06 tff(7584,plain,
% 1.86/2.06 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7461, 7583, 1273, 273])).
% 1.86/2.06 tff(7585,plain,
% 1.86/2.06 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3274, 7584, 7439])).
% 1.86/2.06 tff(7586,plain,
% 1.86/2.06 (b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7585, 7437])).
% 1.86/2.06 tff(7587,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7588,plain,
% 1.86/2.06 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7589,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7588])).
% 1.86/2.06 tff(7590,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, 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(X1, 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(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7589, 7587])).
% 1.86/2.06 tff(7591,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7592,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7591, 7590])).
% 1.86/2.06 tff(7593,plain,
% 1.86/2.06 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7592, 337, 1, 1301, 7586])).
% 1.86/2.06 tff(7594,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7593, 7570])).
% 1.86/2.06 tff(7595,plain,((~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), elem!1)) | (s(s(z)) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7596,plain,
% 1.86/2.06 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7595, 7328, 7354, 5283, 7342, 7365, 7531, 7374, 7509, 7345, 7496, 7353])).
% 1.86/2.06 tff(7597,plain,
% 1.86/2.06 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1150, 7596])).
% 1.86/2.06 tff(7598,plain,
% 1.86/2.06 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7597, 7521])).
% 1.86/2.06 tff(7599,plain,
% 1.86/2.06 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5433, 7598, 7519])).
% 1.86/2.06 tff(7600,plain,
% 1.86/2.06 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[579, 7599, 428])).
% 1.86/2.06 tff(7601,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1133, 7600, 7328])).
% 1.86/2.06 tff(7602,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7603,plain,
% 1.86/2.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(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(s(z)))), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7604,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(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(X1, 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(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(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7603])).
% 1.86/2.06 tff(7605,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(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(X1, 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(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(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7604, 7602])).
% 1.86/2.06 tff(7606,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7607,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7606, 7605])).
% 1.86/2.06 tff(7608,plain,
% 1.86/2.06 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7607, 337, 7509, 7353, 7345])).
% 1.86/2.06 tff(7609,plain,
% 1.86/2.06 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7608, 7601])).
% 1.86/2.06 tff(7610,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[524, 7609])).
% 1.86/2.06 tff(7611,plain,
% 1.86/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7612,plain,
% 1.86/2.06 (((~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(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7613,plain,
% 1.86/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7612])).
% 1.86/2.06 tff(7614,plain,
% 1.86/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7613, 7611])).
% 1.86/2.06 tff(7615,plain,
% 1.86/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7616,plain,
% 1.86/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 1.86/2.06 tff(7617,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7616, 189, 7610, 7374, 7518])).
% 1.86/2.06 tff(7618,plain,((s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7619,plain,
% 1.86/2.06 (r(z, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7618, 5281, 3, 50, 82])).
% 1.86/2.06 tff(7620,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2968, 7619, 49, 50, 82])).
% 1.86/2.06 tff(7621,plain,
% 1.86/2.06 (b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7211, 7620, 82, 50, 5281, 3])).
% 1.86/2.06 tff(7622,plain,
% 1.86/2.06 (elem!1 = s(z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7327, 7620, 3, 50, 5281, 82])).
% 1.86/2.06 tff(7623,plain,
% 1.86/2.06 (b(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6585, 7622, 5283])).
% 1.86/2.06 tff(7624,plain,
% 1.86/2.06 (s(elem!1) = s(s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7622])).
% 1.86/2.06 tff(7625,plain,
% 1.86/2.06 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7624])).
% 1.86/2.06 tff(7626,plain,
% 1.86/2.06 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7625, 7335])).
% 1.86/2.06 tff(7627,plain,
% 1.86/2.06 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[7626])).
% 1.86/2.06 tff(7628,plain,
% 1.86/2.06 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7627])).
% 1.86/2.06 tff(7629,plain,
% 1.86/2.06 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2263, 7628])).
% 1.86/2.06 tff(7630,plain,
% 1.86/2.06 (r(z, elem!1) <=> r(z, s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7622])).
% 1.86/2.06 tff(7631,plain,
% 1.86/2.06 (r(z, s(z)) <=> r(z, elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[7630])).
% 1.86/2.06 tff(7632,plain,
% 1.86/2.06 (r(z, elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7619, 7631])).
% 1.86/2.06 tff(7633,plain,
% 1.86/2.06 (b(s(elem!1), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2045, 7632, 49, 50, 7619, 7621, 147])).
% 1.86/2.06 tff(7634,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3995, 7633, 7629, 7620, 5283, 7623, 7621])).
% 1.86/2.06 tff(7635,plain,(b(z, s(s(s(elem!1)))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7636,plain,
% 1.86/2.06 (b(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7635, 50, 3])).
% 1.86/2.06 tff(7637,plain,
% 1.86/2.06 (r(elem!1, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[322, 2972, 4370])).
% 1.86/2.06 tff(7638,plain,
% 1.86/2.06 (~r(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1709, 7637, 81])).
% 1.86/2.06 tff(7639,plain,
% 1.86/2.06 (b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1759, 7638, 68])).
% 1.86/2.06 tff(7640,plain,
% 1.86/2.06 (~b(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2456, 7639, 925, 3803])).
% 1.86/2.06 tff(7641,plain,
% 1.86/2.06 (~r(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3923, 189, 7637, 118])).
% 1.86/2.06 tff(7642,plain,
% 1.86/2.06 (s(s(s(z))) = elem!1),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2463, 7641, 7640])).
% 1.86/2.06 tff(7643,plain,
% 1.86/2.06 (s(s(s(s(z)))) = s(elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1472, 7642])).
% 1.86/2.06 tff(7644,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2743, 7643, 2972])).
% 1.86/2.06 tff(7645,plain,
% 1.86/2.06 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[427, 7644])).
% 1.86/2.06 tff(7646,plain,
% 1.86/2.06 (~(s(elem!1) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[264, 7644])).
% 1.86/2.06 tff(7647,plain,
% 1.86/2.06 (~(s(z) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[249, 2972])).
% 1.86/2.06 tff(7648,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7649,plain,
% 1.86/2.06 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7650,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7649])).
% 1.86/2.06 tff(7651,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7650, 7648])).
% 1.86/2.06 tff(7652,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7653,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7652, 7651])).
% 1.86/2.06 tff(7654,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7653, 337, 925, 1763, 326, 1925])).
% 1.86/2.06 tff(7655,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7656,plain,
% 1.86/2.06 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7655, 925, 7639, 1925])).
% 1.86/2.06 tff(7657,plain,
% 1.86/2.06 (~r(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1709, 777, 173])).
% 1.86/2.06 tff(7658,plain,
% 1.86/2.06 (b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1759, 7657, 68])).
% 1.86/2.06 tff(7659,plain,
% 1.86/2.06 (~b(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2456, 7658, 925, 1770])).
% 1.86/2.06 tff(7660,plain,
% 1.86/2.06 (s(s(s(z))) = elem!1),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2463, 4124, 7659])).
% 1.86/2.06 tff(7661,plain,
% 1.86/2.06 (s(s(s(s(z)))) = s(elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1472, 7660])).
% 1.86/2.06 tff(7662,plain,
% 1.86/2.06 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4552, 7661])).
% 1.86/2.06 tff(7663,plain,
% 1.86/2.06 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2074, 1735, 118, 173, 7658, 925])).
% 1.86/2.06 tff(7664,plain,
% 1.86/2.06 (s(s(s(s(z)))) = elem!1),
% 1.86/2.06 inference(transitivity,[status(thm)],[1470, 251])).
% 1.86/2.06 tff(7665,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[853, 7664])).
% 1.86/2.06 tff(7666,plain,((~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7667,plain,
% 1.86/2.06 (~(s(elem!1) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7666, 7660, 7663])).
% 1.86/2.06 tff(7668,plain,
% 1.86/2.06 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[5723])).
% 1.86/2.06 tff(7669,plain,
% 1.86/2.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1469, 7668])).
% 1.86/2.06 tff(7670,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2470, 7669])).
% 1.86/2.06 tff(7671,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7672,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7671, 7660, 2451])).
% 1.86/2.06 tff(7673,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[350, 7672, 984])).
% 1.86/2.06 tff(7674,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2743, 7661, 247])).
% 1.86/2.06 tff(7675,plain,
% 1.86/2.06 (~b(s(elem!1), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2166, 273, 777, 172, 1735, 352])).
% 1.86/2.06 tff(7676,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[898, 7675, 5208, 50])).
% 1.86/2.06 tff(7677,plain,((~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7678,plain,
% 1.86/2.06 (~r(s(elem!1), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7677, 7674, 777, 50, 1735, 7673])).
% 1.86/2.06 tff(7679,plain,
% 1.86/2.06 (b(s(elem!1), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[270, 7678, 7667])).
% 1.86/2.06 tff(7680,plain,
% 1.86/2.06 (~(elem!1 = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[281, 7672])).
% 1.86/2.06 tff(7681,plain,
% 1.86/2.06 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[632, 7680])).
% 1.86/2.06 tff(7682,plain,
% 1.86/2.06 (~b(s(elem!1), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3968, 337, 925, 7658, 7679])).
% 1.86/2.06 tff(7683,plain,
% 1.86/2.06 (r(s(elem!1), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[378, 43, 114, 7682])).
% 1.86/2.07 tff(7684,plain,
% 1.86/2.07 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4470, 7683, 925, 7681, 7679, 7658])).
% 1.86/2.07 tff(7685,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[714, 7684, 7662])).
% 1.86/2.07 tff(7686,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6865, 189, 1735, 7685])).
% 1.86/2.07 tff(7687,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4520, 43, 135, 7686])).
% 1.86/2.07 tff(7688,plain,
% 1.86/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7689,plain,
% 1.86/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7690,plain,
% 1.86/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7689, 7688])).
% 1.86/2.07 tff(7691,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7690, 189, 7673, 7685])).
% 1.86/2.07 tff(7692,plain,
% 1.86/2.07 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3128, 7674])).
% 1.86/2.07 tff(7693,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4497, 43, 7692, 7691])).
% 1.86/2.07 tff(7694,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2153, 7673, 777])).
% 1.86/2.07 tff(7695,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[227, 43, 7694, 213])).
% 1.86/2.07 tff(7696,plain,
% 1.86/2.07 (~r(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2164, 189, 7673, 1735])).
% 1.86/2.07 tff(7697,plain,
% 1.86/2.07 (b(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1970, 7696])).
% 1.86/2.07 tff(7698,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7699,plain,
% 1.86/2.07 (((~b(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(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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7700,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7699])).
% 1.86/2.07 tff(7701,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7700, 7698])).
% 1.86/2.07 tff(7702,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7703,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7702, 7701])).
% 1.86/2.07 tff(7704,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7703, 337, 7697, 7695, 7693, 7687])).
% 1.86/2.07 tff(7705,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7706,plain,
% 1.86/2.07 (~r(s(z), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7705, 925, 7637, 50, 7656, 2972, 118, 81])).
% 1.86/2.07 tff(7707,plain,
% 1.86/2.07 (b(s(z), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[727, 7706, 7647])).
% 1.86/2.07 tff(7708,plain,
% 1.86/2.07 (~b(z, s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2717, 2520, 1763, 925])).
% 1.86/2.07 tff(7709,plain,
% 1.86/2.07 (r(z, s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[395, 7708])).
% 1.86/2.07 tff(7710,plain,
% 1.86/2.07 (~r(s(elem!1), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2355, 7709, 173])).
% 1.86/2.07 tff(7711,plain,
% 1.86/2.07 (b(s(elem!1), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[898, 7710, 50])).
% 1.86/2.07 tff(7712,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7713,plain,
% 1.86/2.07 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7714,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7713])).
% 1.86/2.07 tff(7715,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7714, 7712])).
% 1.86/2.07 tff(7716,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7717,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7716, 7715])).
% 1.86/2.07 tff(7718,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7717, 337, 925, 1763, 2520, 7711, 791])).
% 1.86/2.07 tff(7719,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7720,plain,
% 1.86/2.07 (~b(s(elem!1), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7719, 925, 7639, 7707, 50, 81])).
% 1.86/2.07 tff(7721,plain,
% 1.86/2.07 (r(s(elem!1), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[270, 7720, 7646])).
% 1.86/2.07 tff(7722,plain,
% 1.86/2.07 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7671, 7642, 2451])).
% 1.86/2.07 tff(7723,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[350, 7722, 7656])).
% 1.86/2.07 tff(7724,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[358, 7721, 7723])).
% 1.86/2.07 tff(7725,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[363, 7724, 7644])).
% 1.86/2.07 tff(7726,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7727,plain,
% 1.86/2.07 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(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), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7728,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(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), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7727])).
% 1.86/2.07 tff(7729,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(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), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7728, 7726])).
% 1.86/2.07 tff(7730,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(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), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7731,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7730, 7729])).
% 1.86/2.07 tff(7732,plain,
% 1.86/2.07 (~b(s(elem!1), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7731, 337, 365, 638, 1925])).
% 1.86/2.07 tff(7733,plain,
% 1.86/2.07 (r(s(elem!1), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[378, 43, 114, 7732])).
% 1.86/2.07 tff(7734,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2153, 4406, 352])).
% 1.86/2.07 tff(7735,plain,
% 1.86/2.07 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[227, 43, 7734])).
% 1.86/2.07 tff(7736,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7735, 369])).
% 1.86/2.07 tff(7737,plain,
% 1.86/2.07 (~r(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4481, 7736, 638, 365, 50, 7733])).
% 1.86/2.07 tff(7738,plain,
% 1.86/2.07 (b(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[963, 7737])).
% 1.86/2.07 tff(7739,plain,
% 1.86/2.07 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7740,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7739])).
% 1.86/2.07 tff(7741,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7740, 2336])).
% 1.86/2.07 tff(7742,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7743,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7742, 7741])).
% 1.86/2.07 tff(7744,plain,
% 1.86/2.07 (~b(s(z), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7743, 337, 925, 1763, 7738])).
% 1.86/2.07 tff(7745,plain,
% 1.86/2.07 (r(s(z), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[727, 7744, 272])).
% 1.86/2.07 tff(7746,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(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(X1, 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), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7747,plain,
% 1.86/2.07 (((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), z)) | (~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7748,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), z)) | (~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(X1, 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), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7747])).
% 1.86/2.07 tff(7749,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), z)) | (~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(X1, 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), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7748, 7746])).
% 1.86/2.07 tff(7750,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7751,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7750, 7749])).
% 1.86/2.07 tff(7752,plain,
% 1.86/2.07 (~b(s(elem!1), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7751, 337, 365, 638, 1925, 7738, 7736])).
% 1.86/2.07 tff(7753,plain,
% 1.86/2.07 (r(s(elem!1), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[898, 7752, 50])).
% 1.86/2.07 tff(7754,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2097, 189, 273, 7753, 7745])).
% 1.86/2.07 tff(7755,plain,((elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7756,plain,
% 1.86/2.07 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7755, 7725, 1925, 4370, 2972, 7639, 925, 50, 7723, 7721])).
% 1.86/2.07 tff(7757,plain,
% 1.86/2.07 (r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[579, 7756, 7645])).
% 1.86/2.07 tff(7758,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[991, 189, 7721, 7723, 7757])).
% 1.86/2.07 tff(7759,plain,((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7760,plain,
% 1.86/2.07 (~b(z, elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7759, 4370, 1925, 50, 118, 69])).
% 1.86/2.07 tff(7761,plain,
% 1.86/2.07 (r(z, elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[921, 7760, 61])).
% 1.86/2.07 tff(7762,plain,
% 1.86/2.07 (~r(elem!1, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[785, 7761, 81])).
% 1.86/2.07 tff(7763,plain,
% 1.86/2.07 (elem!1 = s(z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[322, 7762, 4370])).
% 1.86/2.07 tff(7764,plain,
% 1.86/2.07 (b(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3403, 7763, 1925])).
% 1.86/2.07 tff(7765,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.07 tff(7766,plain,
% 1.86/2.07 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(z))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.07 tff(7767,plain,
% 1.86/2.07 ((s(s(s(s(z)))) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7766, 843])).
% 1.86/2.07 tff(7768,plain,
% 1.86/2.07 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.86/2.07 inference(symmetry,[status(thm)],[7767])).
% 1.86/2.07 tff(7769,plain,
% 1.86/2.07 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7768])).
% 1.86/2.07 tff(7770,plain,
% 1.86/2.07 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[516, 7769])).
% 1.86/2.07 tff(7771,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.86/2.07 tff(7772,plain,
% 1.86/2.07 (~b(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1795, 2, 1659, 1592])).
% 1.86/2.07 tff(7773,plain,
% 1.86/2.07 (r(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1792, 7772])).
% 1.86/2.07 tff(7774,plain,
% 1.86/2.07 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2023, 7773, 173])).
% 1.86/2.07 tff(7775,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[851, 7774])).
% 1.86/2.07 tff(7776,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, 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)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, 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)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7777,plain,
% 1.86/2.07 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, 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)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7778,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(z, 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)))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7777])).
% 1.86/2.07 tff(7779,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(z, 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)))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7778, 7776])).
% 1.86/2.08 tff(7780,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(7781,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7780, 7779])).
% 1.86/2.08 tff(7782,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7781, 337, 1, 2, 7775, 1592, 1659, 7771])).
% 1.86/2.08 tff(7783,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7784,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7783, 1, 1592, 1770, 201, 173])).
% 1.86/2.08 tff(7785,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[548, 7784])).
% 1.86/2.08 tff(7786,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3611, 189, 1339, 811, 118])).
% 1.86/2.08 tff(7787,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7788,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7787, 7785, 118])).
% 1.86/2.08 tff(7789,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[851, 7788])).
% 1.86/2.08 tff(7790,plain,
% 1.86/2.08 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2027, 7785, 118])).
% 1.86/2.08 tff(7791,plain,
% 1.86/2.08 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1150, 7790])).
% 1.86/2.08 tff(7792,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7793,plain,
% 1.86/2.08 (((~b(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(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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7794,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7793])).
% 1.86/2.08 tff(7795,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7794, 7792])).
% 1.86/2.08 tff(7796,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(7797,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7796, 7795])).
% 1.86/2.08 tff(7798,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7797, 337, 1, 7791, 7789, 1592])).
% 1.86/2.08 tff(7799,plain,((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7800,plain,
% 1.86/2.08 (~b(s(z), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7799, 7764, 118, 81])).
% 1.86/2.08 tff(7801,plain,
% 1.86/2.08 (~b(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6686, 7800, 7763])).
% 1.86/2.08 tff(7802,plain,
% 1.86/2.08 (r(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1759, 7801, 68])).
% 1.86/2.08 tff(7803,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[1169, 1162])).
% 1.86/2.08 tff(7804,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1795, 3864, 1659, 1592])).
% 1.86/2.08 tff(7805,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[548, 7804])).
% 1.86/2.08 tff(7806,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3611, 189, 7805, 7803, 118])).
% 1.86/2.08 tff(7807,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7808,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7807, 7802, 7763, 3803, 7764, 118])).
% 1.86/2.08 tff(7809,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[857, 7808, 7770])).
% 1.86/2.08 tff(7810,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7809, 7765])).
% 1.86/2.08 tff(7811,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.08 tff(7812,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[7811])).
% 1.86/2.08 tff(7813,plain,
% 1.86/2.08 (s(elem!1) = s(s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.08 tff(7814,plain,
% 1.86/2.08 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7813])).
% 1.86/2.08 tff(7815,plain,
% 1.86/2.08 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7814])).
% 1.86/2.08 tff(7816,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7815])).
% 1.86/2.08 tff(7817,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7816])).
% 1.86/2.08 tff(7818,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[7765, 7817, 7812])).
% 1.86/2.08 tff(7819,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7809, 7818])).
% 1.86/2.08 tff(7820,plain,
% 1.86/2.08 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7814, 7763])).
% 1.86/2.08 tff(7821,plain,
% 1.86/2.08 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[7820])).
% 1.86/2.08 tff(7822,plain,
% 1.86/2.08 (r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[118, 7821])).
% 1.86/2.08 tff(7823,plain,
% 1.86/2.08 (s(z) = elem!1),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7763, 120])).
% 1.86/2.08 tff(7824,plain,
% 1.86/2.08 (~r(s(elem!1), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2010, 7823, 7761, 7822])).
% 1.86/2.08 tff(7825,plain,
% 1.86/2.08 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1799])).
% 1.86/2.08 tff(7826,plain,
% 1.86/2.08 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7825])).
% 1.86/2.08 tff(7827,plain,
% 1.86/2.08 ((~b(z, elem!1)) <=> (~b(z, s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7826])).
% 1.86/2.08 tff(7828,plain,
% 1.86/2.08 (~b(z, s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6583, 7827])).
% 1.86/2.08 tff(7829,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1925, 7828])).
% 1.86/2.08 tff(7830,plain,((~(s(elem!1) = elem!1)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7831,plain,
% 1.86/2.08 (~(s(elem!1) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7830, 7760, 1925])).
% 1.86/2.08 tff(7832,plain,
% 1.86/2.08 (~(elem!1 = s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[980, 7831])).
% 1.86/2.08 tff(7833,plain,
% 1.86/2.08 (~r(s(z), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1743, 7761, 81])).
% 1.86/2.08 tff(7834,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7815, 7813])).
% 1.86/2.08 tff(7835,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7834, 7335])).
% 1.86/2.08 tff(7836,plain,
% 1.86/2.08 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7835])).
% 1.86/2.08 tff(7837,plain,
% 1.86/2.08 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7836])).
% 1.86/2.08 tff(7838,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2263, 7837])).
% 1.86/2.08 tff(7839,plain,
% 1.86/2.08 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.08 tff(7840,plain,
% 1.86/2.08 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7839])).
% 1.86/2.08 tff(7841,plain,
% 1.86/2.08 (~r(s(elem!1), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7824, 7840])).
% 1.86/2.08 tff(7842,plain,
% 1.86/2.08 (~b(s(elem!1), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3763, 7841, 7762, 81, 7838, 7824, 7833])).
% 1.86/2.08 tff(7843,plain,
% 1.86/2.08 (r(s(elem!1), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1262, 7842, 7763])).
% 1.86/2.08 tff(7844,plain,
% 1.86/2.08 (~r(elem!1, s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1023, 7802, 7843])).
% 1.86/2.08 tff(7845,plain,
% 1.86/2.08 (b(elem!1, s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1015, 7844, 7832])).
% 1.86/2.08 tff(7846,plain,
% 1.86/2.08 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[230])).
% 1.86/2.08 tff(7847,plain,
% 1.86/2.08 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7846])).
% 1.86/2.08 tff(7848,plain,
% 1.86/2.08 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[231])).
% 1.86/2.08 tff(7849,plain,
% 1.86/2.08 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7848])).
% 1.86/2.08 tff(7850,plain,
% 1.86/2.08 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7849, 7847])).
% 1.86/2.08 tff(7851,plain,
% 1.86/2.08 ((~b(s(z), s(s(z)))) <=> (~b(elem!1, s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7850])).
% 1.86/2.08 tff(7852,plain,
% 1.86/2.08 (~b(elem!1, s(elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3381, 7851])).
% 1.86/2.08 tff(7853,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[982, 7852])).
% 1.86/2.08 tff(7854,plain,(b(s(z), s(s(z))) | (~b(elem!1, s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7855,plain,
% 1.86/2.08 (b(s(z), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7854, 7845, 7763])).
% 1.86/2.08 tff(7856,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[233, 231])).
% 1.86/2.08 tff(7857,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7856, 7335])).
% 1.86/2.08 tff(7858,plain,
% 1.86/2.08 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(symmetry,[status(thm)],[7857])).
% 1.86/2.08 tff(7859,plain,
% 1.86/2.08 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7858])).
% 1.86/2.08 tff(7860,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2263, 7859])).
% 1.86/2.08 tff(7861,plain,
% 1.86/2.08 (b(z, s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3170, 7772, 230, 7860, 3062, 274, 326])).
% 1.86/2.08 tff(7862,plain,
% 1.86/2.08 (b(z, s(s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7861, 3100])).
% 1.86/2.08 tff(7863,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), 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)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), 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)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7864,plain,
% 1.86/2.08 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(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(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), 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)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7865,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), 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)))), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7864])).
% 1.86/2.08 tff(7866,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), 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)))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7865, 7863])).
% 1.86/2.08 tff(7867,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(7868,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7867, 7866])).
% 1.86/2.08 tff(7869,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7868, 337, 2, 1231, 1592, 3477, 7862, 1659])).
% 1.86/2.08 tff(7870,plain,((~b(s(s(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(z)))) | (~b(s(s(s(z))), z)) | (~(elem!1 = s(z))) | r(s(elem!1), elem!1) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7871,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7870, 7810, 7764, 7855, 3803, 7763, 7824, 7802, 7819])).
% 1.86/2.08 tff(7872,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[548, 7871])).
% 1.86/2.08 tff(7873,plain,
% 1.86/2.08 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2027, 7872, 118])).
% 1.86/2.08 tff(7874,plain,
% 1.86/2.08 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1150, 7873])).
% 1.86/2.08 tff(7875,plain,
% 1.86/2.08 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[3116])).
% 1.86/2.08 tff(7876,plain,
% 1.86/2.08 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6712, 7875])).
% 1.86/2.08 tff(7877,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.86/2.08 tff(7878,plain,
% 1.86/2.08 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 1.86/2.08 tff(7879,plain,
% 1.86/2.08 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3128, 7860])).
% 1.86/2.08 tff(7880,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7879, 7878])).
% 1.86/2.08 tff(7881,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7882,plain,
% 1.86/2.08 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7881, 7763])).
% 1.86/2.08 tff(7883,plain,
% 1.86/2.08 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7813])).
% 1.86/2.08 tff(7884,plain,
% 1.86/2.08 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7763])).
% 1.86/2.08 tff(7885,plain,
% 1.86/2.08 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7884, 7883])).
% 1.86/2.08 tff(7886,plain,
% 1.86/2.08 (b(s(elem!1), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[270, 7824, 7831])).
% 1.86/2.08 tff(7887,plain,
% 1.86/2.08 (b(s(s(z)), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7886, 7885])).
% 1.86/2.08 tff(7888,plain,
% 1.86/2.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3393, 337, 7810, 7855, 7887])).
% 1.86/2.08 tff(7889,plain,
% 1.86/2.08 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2268, 7888])).
% 1.86/2.08 tff(7890,plain,
% 1.86/2.08 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7815])).
% 1.86/2.08 tff(7891,plain,
% 1.86/2.08 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7890])).
% 1.86/2.08 tff(7892,plain,
% 1.86/2.08 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7891, 6663])).
% 1.86/2.08 tff(7893,plain,
% 1.86/2.08 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7892])).
% 1.86/2.08 tff(7894,plain,
% 1.86/2.08 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[116, 7893])).
% 1.86/2.08 tff(7895,plain,
% 1.86/2.08 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7891])).
% 1.86/2.08 tff(7896,plain,
% 1.86/2.08 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[116, 7895])).
% 1.86/2.08 tff(7897,plain,
% 1.86/2.08 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7890, 7813])).
% 1.86/2.08 tff(7898,plain,
% 1.86/2.08 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7897, 7355])).
% 1.86/2.08 tff(7899,plain,
% 1.86/2.08 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7898])).
% 1.86/2.08 tff(7900,plain,
% 1.86/2.08 ((~b(z, elem!1)) <=> (~b(z, s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[924])).
% 1.86/2.08 tff(7901,plain,
% 1.86/2.08 (~b(z, s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6583, 7900])).
% 1.86/2.08 tff(7902,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1925, 7901])).
% 1.86/2.08 tff(7903,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(7904,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7903, 7760, 1925])).
% 1.86/2.08 tff(7905,plain,
% 1.86/2.08 (~(elem!1 = s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[281, 7904])).
% 1.86/2.08 tff(7906,plain,
% 1.86/2.08 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[632, 7905])).
% 1.86/2.08 tff(7907,plain,
% 1.86/2.08 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7906, 7899])).
% 1.86/2.08 tff(7908,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.08 tff(7909,plain,
% 1.86/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7910,plain,
% 1.86/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(7911,plain,
% 1.86/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7910, 7909])).
% 1.86/2.08 tff(7912,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7911, 189, 1339, 7908])).
% 1.86/2.08 tff(7913,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6709, 7912, 7544])).
% 1.86/2.08 tff(7914,plain,
% 1.86/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7915,plain,
% 1.86/2.08 (((~r(s(s(s(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(s(s(s(z)))))))) <=> ((~r(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(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7916,plain,
% 1.86/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7915])).
% 1.86/2.08 tff(7917,plain,
% 1.86/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[7916, 7914])).
% 1.86/2.08 tff(7918,plain,
% 1.86/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(7919,plain,
% 1.86/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))), s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7918, 7917])).
% 1.86/2.08 tff(7920,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7919, 189, 1339, 7908])).
% 1.86/2.08 tff(7921,plain,
% 1.86/2.08 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2489, 7920, 2477])).
% 1.86/2.08 tff(7922,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3347, 189, 7908, 4222])).
% 1.86/2.08 tff(7923,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3299, 7922, 7385])).
% 1.86/2.08 tff(7924,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(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(X1, 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))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7925,plain,
% 1.86/2.09 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7926,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(X1, 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))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7925])).
% 1.86/2.09 tff(7927,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(X1, 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))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[7926, 7924])).
% 1.86/2.09 tff(7928,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(7929,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7928, 7927])).
% 1.86/2.09 tff(7930,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7929, 337, 7923, 1659, 5123, 7921, 7913])).
% 1.86/2.09 tff(7931,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (s(s(z)) = s(s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | (s(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(7932,plain,
% 1.86/2.09 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7931, 7872, 7907, 7896, 7894, 7889, 3803])).
% 1.86/2.09 tff(7933,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6726, 7932, 7882])).
% 1.86/2.09 tff(7934,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7935,plain,
% 1.86/2.09 (((~b(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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7936,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7935])).
% 1.86/2.09 tff(7937,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.09 inference(transitivity,[status(thm)],[7936, 7934])).
% 1.86/2.09 tff(7938,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(7939,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7938, 7937])).
% 1.86/2.09 tff(7940,plain,
% 1.86/2.09 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7939, 337, 1275, 1231, 1592, 3242])).
% 1.86/2.09 tff(7941,plain,
% 1.86/2.09 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7940, 3504])).
% 1.86/2.09 tff(7942,plain,
% 1.86/2.09 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[230, 3107])).
% 1.86/2.09 tff(7943,plain,
% 1.86/2.09 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[7942])).
% 1.86/2.09 tff(7944,plain,
% 1.86/2.09 (((~![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)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7945,plain,
% 1.86/2.09 ((~![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)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(7946,plain,
% 1.86/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7945, 7944])).
% 1.86/2.09 tff(7947,plain,
% 1.86/2.09 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7946, 43])).
% 1.86/2.09 tff(7948,plain,
% 1.86/2.09 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7947, 2331])).
% 1.86/2.09 tff(7949,plain,
% 1.86/2.09 (r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7948, 3269])).
% 1.86/2.09 tff(7950,plain,
% 1.86/2.09 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7949, 7943])).
% 1.86/2.09 tff(7951,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3285, 7950, 274])).
% 1.86/2.09 tff(7952,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[663, 7951, 7941])).
% 1.86/2.09 tff(7953,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(7954,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7953, 7933, 7874, 7763, 7802, 7810, 7764])).
% 1.86/2.09 tff(7955,plain,(b(elem!1, s(z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(7956,plain,
% 1.86/2.09 (b(elem!1, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7955, 69, 7636, 50, 49])).
% 1.86/2.09 tff(7957,plain,
% 1.86/2.09 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5572, 327, 3])).
% 1.86/2.09 tff(7958,plain,
% 1.86/2.09 (~(s(s(s(z))) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1472, 7957])).
% 1.86/2.09 tff(7959,plain,
% 1.86/2.09 (~r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[195, 189, 173, 49])).
% 1.86/2.09 tff(7960,plain,
% 1.86/2.09 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[199, 43, 7959])).
% 1.86/2.09 tff(7961,plain,
% 1.86/2.09 (b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7960, 179])).
% 1.86/2.09 tff(7962,plain,
% 1.86/2.09 (~r(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1768, 173, 49])).
% 1.86/2.09 tff(7963,plain,
% 1.86/2.09 (b(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1498, 7962])).
% 1.86/2.09 tff(7964,plain,
% 1.86/2.09 (~b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2932, 337, 1763, 7963, 7961])).
% 1.86/2.09 tff(7965,plain,
% 1.86/2.09 (r(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2463, 7964, 7958])).
% 1.86/2.09 tff(7966,plain,
% 1.86/2.09 (~r(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4123, 7965, 49])).
% 1.86/2.09 tff(7967,plain,
% 1.86/2.09 (b(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[727, 7966, 272])).
% 1.86/2.09 tff(7968,plain,
% 1.86/2.09 (~r(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4123, 2465, 118])).
% 1.86/2.09 tff(7969,plain,
% 1.86/2.09 (b(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[727, 7968, 272])).
% 1.86/2.09 tff(7970,plain,
% 1.86/2.09 (~b(z, elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7719, 3948, 1763, 7969, 50, 173])).
% 1.86/2.09 tff(7971,plain,
% 1.86/2.09 (r(z, elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[921, 7970, 61])).
% 1.86/2.09 tff(7972,plain,
% 1.86/2.09 (~r(elem!1, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[785, 7971, 173])).
% 1.86/2.09 tff(7973,plain,
% 1.86/2.09 (~b(s(elem!1), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2594, 7972, 247, 7968, 3948])).
% 1.86/2.09 tff(7974,plain,
% 1.86/2.09 (r(s(elem!1), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[898, 7973, 50])).
% 1.86/2.09 tff(7975,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4845, 189, 7974, 118])).
% 1.86/2.09 tff(7976,plain,
% 1.86/2.09 (~r(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2355, 7974, 173])).
% 1.86/2.09 tff(7977,plain,
% 1.86/2.09 (b(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[395, 7976])).
% 1.86/2.09 tff(7978,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7979,plain,
% 1.86/2.09 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(7980,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7979])).
% 1.86/2.09 tff(7981,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[7980, 7978])).
% 1.86/2.09 tff(7982,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(7983,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7982, 7981])).
% 1.86/2.09 tff(7984,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7983, 337, 1763, 7977, 3948, 1770, 201])).
% 1.86/2.09 tff(7985,plain,
% 1.86/2.09 (s(s(s(z))) = s(elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4678, 43, 7984, 7975])).
% 1.86/2.09 tff(7986,plain,
% 1.86/2.09 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7985])).
% 1.86/2.09 tff(7987,plain,
% 1.86/2.09 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[7986])).
% 1.86/2.09 tff(7988,plain,
% 1.86/2.09 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7987])).
% 1.86/2.09 tff(7989,plain,
% 1.86/2.09 (~r(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3062, 7988])).
% 1.86/2.09 tff(7990,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2465, 7989])).
% 1.86/2.09 tff(7991,plain,(r(s(elem!1), elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(7992,plain,
% 1.86/2.09 (r(s(elem!1), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7991, 265, 49, 1763, 173, 50, 247, 7965])).
% 1.86/2.09 tff(7993,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2483, 189, 7992, 7965])).
% 1.86/2.09 tff(7994,plain,
% 1.86/2.09 (r(z, elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[921, 6583, 61])).
% 1.86/2.09 tff(7995,plain,
% 1.86/2.09 (~r(s(elem!1), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[374, 7994, 273])).
% 1.86/2.09 tff(7996,plain,
% 1.86/2.09 (b(s(elem!1), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[378, 43, 114, 7995])).
% 1.86/2.09 tff(7997,plain,
% 1.86/2.09 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7903, 6583, 7636])).
% 1.86/2.09 tff(7998,plain,
% 1.86/2.09 (~r(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1748, 7994, 273])).
% 1.86/2.09 tff(7999,plain,
% 1.86/2.09 (b(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[395, 7998])).
% 1.86/2.09 tff(8000,plain,
% 1.86/2.09 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1927, 2392, 1925, 600])).
% 1.86/2.09 tff(8001,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[363, 8000, 172])).
% 1.86/2.09 tff(8002,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[358, 8001, 273])).
% 1.86/2.09 tff(8003,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[350, 8002, 276])).
% 1.86/2.09 tff(8004,plain,
% 1.86/2.09 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1977, 337, 327, 8003, 791])).
% 1.86/2.09 tff(8005,plain,
% 1.86/2.09 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[310, 43, 211, 8004])).
% 1.86/2.09 tff(8006,plain,
% 1.86/2.09 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5433, 8005, 788])).
% 1.86/2.09 tff(8007,plain,
% 1.86/2.09 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[579, 8006, 428])).
% 1.86/2.09 tff(8008,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8009,plain,
% 1.86/2.09 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~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))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8010,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8009])).
% 1.86/2.09 tff(8011,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8010, 8008])).
% 1.86/2.09 tff(8012,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8013,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8012, 8011])).
% 1.86/2.09 tff(8014,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8013, 337, 365, 600, 638, 1925])).
% 1.86/2.09 tff(8015,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8016,plain,
% 1.86/2.09 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8015, 638, 600, 1925])).
% 1.86/2.09 tff(8017,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[363, 8016, 172])).
% 1.86/2.09 tff(8018,plain,
% 1.86/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8019,plain,
% 1.86/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8020,plain,
% 1.86/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8019, 8018])).
% 1.86/2.09 tff(8021,plain,
% 1.86/2.09 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8020, 189])).
% 1.86/2.09 tff(8022,plain,
% 1.86/2.09 (~r(elem!1, s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8021, 8017, 2543])).
% 1.86/2.09 tff(8023,plain,
% 1.86/2.09 (b(elem!1, s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[295, 43, 8022, 282])).
% 1.86/2.09 tff(8024,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[358, 8017, 273])).
% 1.86/2.09 tff(8025,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[350, 8024, 276])).
% 1.86/2.09 tff(8026,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8027,plain,
% 1.86/2.09 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8028,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8027])).
% 1.86/2.09 tff(8029,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8028, 8026])).
% 1.86/2.10 tff(8030,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(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))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8031,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8030, 8029])).
% 1.86/2.10 tff(8032,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8031, 337, 8025, 600, 638, 1925, 8023])).
% 1.86/2.10 tff(8033,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8034,plain,
% 1.86/2.10 (~r(elem!1, s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8033, 8007, 1925, 276, 600, 273, 172])).
% 1.86/2.10 tff(8035,plain,
% 1.86/2.10 (b(elem!1, s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1015, 8034, 981])).
% 1.86/2.10 tff(8036,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8037,plain,
% 1.86/2.10 (((~b(elem!1, s(elem!1))) | (~b(z, 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))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8038,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8037])).
% 1.86/2.10 tff(8039,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8038, 8036])).
% 1.86/2.10 tff(8040,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, 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)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8041,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 1.86/2.10 tff(8042,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8041, 337, 8003, 600, 8007, 1925, 8035, 2392])).
% 1.86/2.10 tff(8043,plain,((~r(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8044,plain,
% 1.86/2.10 (~r(s(elem!1), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8043, 7999, 7636, 173, 273, 172, 327, 791, 7997])).
% 1.86/2.10 tff(8045,plain,
% 1.86/2.10 (b(s(elem!1), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[898, 8044, 50])).
% 1.86/2.10 tff(8046,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8047,plain,
% 1.86/2.10 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8048,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8047])).
% 1.86/2.10 tff(8049,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8048, 8046])).
% 1.86/2.10 tff(8050,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8051,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8050, 8049])).
% 1.86/2.10 tff(8052,plain,
% 1.86/2.10 (~b(s(s(s(z))), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8051, 337, 7999, 8045, 7996, 7963])).
% 1.86/2.10 tff(8053,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.86/2.10 tff(8054,plain,
% 1.86/2.10 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4678, 43, 8053])).
% 1.86/2.10 tff(8055,plain,
% 1.86/2.10 (s(s(s(z))) = s(elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8054, 8052])).
% 1.86/2.10 tff(8056,plain,
% 1.86/2.10 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8055])).
% 1.86/2.10 tff(8057,plain,
% 1.86/2.10 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.86/2.10 inference(symmetry,[status(thm)],[8056])).
% 1.86/2.10 tff(8058,plain,
% 1.86/2.10 (b(s(s(s(z))), s(z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8045, 8057])).
% 1.86/2.10 tff(8059,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3, 8058])).
% 1.86/2.10 tff(8060,plain,(b(z, elem!1) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8061,plain,
% 1.86/2.10 (b(z, elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8060, 7993, 3, 50, 173, 7992, 172, 327, 7967])).
% 1.86/2.10 tff(8062,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[7655, 8061, 1763, 7636])).
% 1.86/2.10 tff(8063,plain,
% 1.86/2.10 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[801, 157, 247])).
% 1.86/2.10 tff(8064,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[350, 8063, 984])).
% 1.86/2.10 tff(8065,plain,
% 1.86/2.10 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[991, 189, 273, 8064])).
% 1.86/2.10 tff(8066,plain,
% 1.86/2.10 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[358, 8064, 273])).
% 1.86/2.10 tff(8067,plain,
% 1.86/2.10 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[363, 8066, 172])).
% 1.86/2.10 tff(8068,plain,
% 1.86/2.10 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2475])).
% 1.86/2.10 tff(8069,plain,
% 1.86/2.10 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[8068])).
% 1.86/2.10 tff(8070,plain,
% 1.86/2.10 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8069])).
% 1.86/2.10 tff(8071,plain,
% 1.86/2.10 (~(s(s(s(z))) = s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2510, 157, 50])).
% 1.86/2.10 tff(8072,plain,
% 1.86/2.10 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8071, 8070])).
% 1.86/2.10 tff(8073,plain,
% 1.86/2.10 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2499, 8072, 2465, 157, 8067, 2451, 8064, 273])).
% 1.86/2.10 tff(8074,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[579, 8073, 8065, 428])).
% 1.86/2.10 tff(8075,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8076,plain,
% 1.86/2.10 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8075, 7992, 7965, 172, 8062, 50, 247])).
% 1.86/2.10 tff(8077,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1856, 189, 173, 811, 1115])).
% 1.86/2.10 tff(8078,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8079,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8078, 1115, 173])).
% 1.86/2.10 tff(8080,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[851, 8079])).
% 1.86/2.10 tff(8081,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8082,plain,
% 1.86/2.10 (((~b(elem!1, z)) | (~b(elem!1, 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, z)) | (~b(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))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8083,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, 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(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8082])).
% 1.86/2.10 tff(8084,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, 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(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8083, 8081])).
% 1.86/2.10 tff(8085,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, 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)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8086,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 1.86/2.10 tff(8087,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8086, 337, 1763, 327, 791, 8080])).
% 1.86/2.10 tff(8088,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[857, 8087, 853])).
% 1.86/2.10 tff(8089,plain,
% 1.86/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8090,plain,
% 1.86/2.10 (((~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(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8091,plain,
% 1.86/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8090])).
% 1.86/2.10 tff(8092,plain,
% 1.86/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8091, 8089])).
% 1.86/2.10 tff(8093,plain,
% 1.86/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8094,plain,
% 1.86/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 1.86/2.10 tff(8095,plain,
% 1.86/2.10 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8094, 189, 273, 8088])).
% 1.86/2.10 tff(8096,plain,
% 1.86/2.10 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4640, 43, 8095])).
% 1.86/2.10 tff(8097,plain,
% 1.86/2.10 (b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8096, 4630])).
% 1.86/2.10 tff(8098,plain,
% 1.86/2.10 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1580, 1115, 173])).
% 1.86/2.10 tff(8099,plain,
% 1.86/2.10 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1150, 8098])).
% 1.86/2.10 tff(8100,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2939, 189, 8088, 2465])).
% 1.86/2.10 tff(8101,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[524, 8100])).
% 1.86/2.10 tff(8102,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8103,plain,
% 1.86/2.10 (((~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(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8104,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8103])).
% 1.86/2.10 tff(8105,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8104, 8102])).
% 1.86/2.10 tff(8106,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8107,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8106, 8105])).
% 1.86/2.10 tff(8108,plain,
% 1.86/2.10 (~b(s(elem!1), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8107, 337, 8101, 8099, 2, 8097])).
% 1.86/2.10 tff(8109,plain,
% 1.86/2.10 (r(s(elem!1), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[898, 8108, 50])).
% 1.86/2.10 tff(8110,plain,
% 1.86/2.10 (~r(z, s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2355, 8109, 173])).
% 1.86/2.10 tff(8111,plain,
% 1.86/2.10 (b(z, s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[395, 8110])).
% 1.86/2.10 tff(8112,plain,
% 1.86/2.10 (s(s(s(elem!1))) = elem!1),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8043, 8111, 1925, 173, 273, 172, 327, 791, 8109])).
% 1.86/2.10 tff(8113,plain,
% 1.86/2.10 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8112])).
% 1.86/2.10 tff(8114,plain,
% 1.86/2.10 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[8113])).
% 1.86/2.10 tff(8115,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8116,plain,
% 1.86/2.10 (((~b(s(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(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8117,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8116])).
% 1.86/2.10 tff(8118,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8117, 8115])).
% 1.86/2.10 tff(8119,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8120,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8119, 8118])).
% 1.86/2.11 tff(8121,plain,
% 1.86/2.11 (~b(s(elem!1), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8120, 337, 8101, 2, 8097])).
% 1.86/2.11 tff(8122,plain,
% 1.86/2.11 (~r(s(elem!1), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1641, 189, 273, 2465])).
% 1.86/2.11 tff(8123,plain,
% 1.86/2.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8124,plain,
% 1.86/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8125,plain,
% 1.86/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8124, 8123])).
% 1.86/2.11 tff(8126,plain,
% 1.86/2.11 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8125, 43, 8122])).
% 1.86/2.11 tff(8127,plain,
% 1.86/2.11 (s(elem!1) = s(s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8126, 8121])).
% 1.86/2.11 tff(8128,plain,
% 1.86/2.11 (s(s(s(z))) = s(elem!1)),
% 1.86/2.11 inference(symmetry,[status(thm)],[8127])).
% 1.86/2.11 tff(8129,plain,
% 1.86/2.11 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8128, 8114])).
% 1.86/2.11 tff(8130,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[116, 8129])).
% 1.86/2.11 tff(8131,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8132,plain,
% 1.86/2.11 (~r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8131, 2, 173, 273, 172, 327, 791, 50, 1925, 829, 2465, 853, 1763])).
% 1.86/2.11 tff(8133,plain,
% 1.86/2.11 (b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1786, 8132])).
% 1.86/2.11 tff(8134,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1795, 8133, 1659, 2])).
% 1.86/2.11 tff(8135,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1792, 8134])).
% 1.86/2.11 tff(8136,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2023, 8135, 173])).
% 1.86/2.11 tff(8137,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[851, 8136])).
% 1.86/2.11 tff(8138,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~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)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~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)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8139,plain,
% 1.86/2.11 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(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(z, elem!1)) | (~b(s(z), elem!1)) | (~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)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8140,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~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)))), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8139])).
% 1.86/2.11 tff(8141,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~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)))), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8140, 8138])).
% 1.86/2.11 tff(8142,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8143,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8142, 8141])).
% 1.86/2.11 tff(8144,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8143, 337, 925, 791, 2, 8137, 8133, 1659])).
% 1.86/2.11 tff(8145,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8146,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8145, 8061, 7967, 7963, 173, 7992, 172, 327, 50, 7636, 7957, 7965, 8076, 1763])).
% 1.86/2.11 tff(8147,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[548, 8146])).
% 1.86/2.11 tff(8148,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7787, 8147, 49])).
% 1.86/2.11 tff(8149,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[851, 8148])).
% 1.86/2.11 tff(8150,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1812, 189, 1339, 1169, 2465])).
% 1.86/2.11 tff(8151,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8152,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8151, 8147, 7965])).
% 1.86/2.11 tff(8153,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[857, 8152, 8076])).
% 1.86/2.11 tff(8154,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2027, 8147, 49])).
% 1.86/2.11 tff(8155,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1150, 8154])).
% 1.86/2.11 tff(8156,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8157,plain,
% 1.86/2.11 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, 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(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8158,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8157])).
% 1.86/2.11 tff(8159,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8158, 8156])).
% 1.86/2.11 tff(8160,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8161,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8160, 8159])).
% 1.86/2.11 tff(8162,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8161, 337, 327, 8155, 8153, 8149])).
% 1.86/2.11 tff(8163,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (elem!1 = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8164,plain,
% 1.86/2.11 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8163, 1763, 173, 50, 327, 247, 3])).
% 1.86/2.11 tff(8165,plain,
% 1.86/2.11 (~(s(s(z)) = elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[155, 8164, 50])).
% 1.86/2.11 tff(8166,plain,
% 1.86/2.11 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[170, 8164, 50])).
% 1.86/2.11 tff(8167,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7787, 1339, 118])).
% 1.86/2.11 tff(8168,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[851, 8167])).
% 1.86/2.11 tff(8169,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8151, 1339, 2465])).
% 1.86/2.11 tff(8170,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[857, 8169, 853])).
% 1.86/2.11 tff(8171,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2027, 1339, 118])).
% 1.86/2.11 tff(8172,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1150, 8171])).
% 1.86/2.11 tff(8173,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8161, 337, 327, 8172, 8170, 8168])).
% 1.86/2.11 tff(8174,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8175,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8174, 8166, 327, 7965, 49])).
% 1.86/2.11 tff(8176,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[548, 8175])).
% 1.86/2.11 tff(8177,plain,
% 1.86/2.11 (~r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8078, 811, 173])).
% 1.86/2.11 tff(8178,plain,
% 1.86/2.11 (b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1786, 8177])).
% 1.86/2.11 tff(8179,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1795, 8178, 2400, 1659, 2])).
% 1.86/2.11 tff(8180,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8181,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8180, 8176, 7963, 173])).
% 1.86/2.11 tff(8182,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[851, 8181])).
% 1.86/2.11 tff(8183,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8086, 337, 1763, 327, 7967, 8182])).
% 1.86/2.11 tff(8184,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[857, 8183, 8166])).
% 1.86/2.11 tff(8185,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2939, 189, 8184, 7965])).
% 1.86/2.11 tff(8186,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[524, 8185])).
% 1.86/2.11 tff(8187,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8180, 2, 1770, 173])).
% 1.86/2.11 tff(8188,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[851, 8187])).
% 1.86/2.11 tff(8189,plain,
% 1.86/2.11 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3324, 337, 2, 8188, 201])).
% 1.86/2.11 tff(8190,plain,
% 1.86/2.11 (~b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8189, 3243])).
% 1.86/2.11 tff(8191,plain,
% 1.86/2.11 (r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1786, 8190])).
% 1.86/2.11 tff(8192,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1580, 8191, 173])).
% 1.86/2.11 tff(8193,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1150, 8192])).
% 1.86/2.11 tff(8194,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8195,plain,
% 1.86/2.11 (((~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(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(z)), 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)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8196,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8195])).
% 1.86/2.11 tff(8197,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8196, 8194])).
% 1.86/2.11 tff(8198,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8199,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8198, 8197])).
% 1.86/2.11 tff(8200,plain,
% 1.86/2.11 (~b(s(s(z)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8199, 337, 3243, 8193, 2, 1396])).
% 1.86/2.11 tff(8201,plain,
% 1.86/2.11 (r(s(s(z)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2229, 8200])).
% 1.86/2.11 tff(8202,plain,
% 1.86/2.11 (~r(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2253, 8201, 173])).
% 1.86/2.11 tff(8203,plain,
% 1.86/2.11 (~b(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1239, 337, 8193, 8188, 1396])).
% 1.86/2.11 tff(8204,plain,
% 1.86/2.11 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.86/2.11 inference(commutativity,[status(thm)],[])).
% 1.86/2.11 tff(8205,plain,
% 1.86/2.11 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8204])).
% 1.86/2.11 tff(8206,plain,
% 1.86/2.11 (~(s(z) = s(s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2224, 8205])).
% 1.86/2.11 tff(8207,plain,
% 1.86/2.11 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3386, 8206])).
% 1.86/2.11 tff(8208,plain,
% 1.86/2.11 (r(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8207, 8203])).
% 1.86/2.11 tff(8209,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2866, 118, 1274, 173])).
% 1.86/2.11 tff(8210,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1360, 43, 458, 8209])).
% 1.86/2.11 tff(8211,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1389, 189, 118, 3370, 8210])).
% 1.86/2.11 tff(8212,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (s(s(s(z))) = s(s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8213,plain,
% 1.86/2.11 ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8212, 2009])).
% 1.86/2.11 tff(8214,plain,
% 1.86/2.11 (~b(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8213, 8208, 118, 173])).
% 1.86/2.11 tff(8215,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2242, 8214, 8202])).
% 1.86/2.11 tff(8216,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8217,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8216, 8186, 173, 49, 8176])).
% 1.86/2.11 tff(8218,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2268, 8217])).
% 1.86/2.11 tff(8219,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8220,plain,
% 1.86/2.11 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8221,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8220])).
% 1.86/2.11 tff(8222,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8221, 8219])).
% 1.86/2.11 tff(8223,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(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)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8224,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 1.86/2.11 tff(8225,plain,
% 1.86/2.11 (~b(elem!1, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8224, 337, 327, 7967, 8182])).
% 1.86/2.11 tff(8226,plain,
% 1.86/2.11 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2760, 8166])).
% 1.86/2.11 tff(8227,plain,
% 1.86/2.11 (r(elem!1, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2845, 43, 8226, 8225])).
% 1.86/2.11 tff(8228,plain,
% 1.86/2.11 (~r(s(s(z)), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2849, 189, 8227, 8218])).
% 1.86/2.11 tff(8229,plain,
% 1.86/2.11 (b(s(s(z)), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2301, 8228, 8165])).
% 1.86/2.11 tff(8230,plain,
% 1.86/2.11 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3324, 337, 8176, 8182, 7961])).
% 1.86/2.11 tff(8231,plain,
% 1.86/2.11 (~b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8230, 8186])).
% 1.86/2.11 tff(8232,plain,
% 1.86/2.11 (r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1786, 8231])).
% 1.86/2.11 tff(8233,plain,
% 1.86/2.11 (~r(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[4338, 189, 8232, 8218])).
% 1.86/2.11 tff(8234,plain,
% 1.86/2.11 (b(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2242, 8233])).
% 1.86/2.11 tff(8235,plain,
% 1.86/2.11 (~r(z, elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[4746, 189, 8232, 8227])).
% 1.86/2.11 tff(8236,plain,
% 1.86/2.11 (b(z, elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[921, 8235, 61])).
% 1.86/2.11 tff(8237,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8238,plain,
% 1.86/2.12 (((~b(z, elem!1)) | (~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)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8239,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8238])).
% 1.86/2.12 tff(8240,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X1, 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)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8239, 8237])).
% 1.86/2.12 tff(8241,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8242,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8241, 8240])).
% 1.86/2.12 tff(8243,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8242, 337, 8236, 1763, 8234, 8229])).
% 1.86/2.12 tff(8244,plain,((~b(elem!1, z)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(8245,plain,
% 1.86/2.12 (~b(elem!1, z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8244, 247, 327, 50, 173, 3])).
% 1.86/2.12 tff(8246,plain,
% 1.86/2.12 (r(elem!1, z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1759, 8245, 68])).
% 1.86/2.12 tff(8247,plain,
% 1.86/2.12 (~r(elem!1, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1709, 8246, 173])).
% 1.86/2.12 tff(8248,plain,
% 1.86/2.12 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(monotonicity,[status(thm)],[157])).
% 1.86/2.12 tff(8249,plain,
% 1.86/2.12 (r(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[1339, 8248])).
% 1.86/2.12 tff(8250,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2461, 8249])).
% 1.86/2.12 tff(8251,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(z))), elem!1) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(8252,plain,
% 1.86/2.12 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8251, 2461, 1339])).
% 1.86/2.12 tff(8253,plain,
% 1.86/2.12 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2760, 8252])).
% 1.86/2.12 tff(8254,plain,
% 1.86/2.12 (((~b(s(s(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(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(z), 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))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8255,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8254])).
% 1.86/2.12 tff(8256,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8255, 5775])).
% 1.86/2.12 tff(8257,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8258,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8257, 8256])).
% 1.86/2.12 tff(8259,plain,
% 1.86/2.12 (~b(elem!1, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8258, 337, 327, 8172, 8168])).
% 1.86/2.12 tff(8260,plain,
% 1.86/2.12 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2845, 43, 8259])).
% 1.86/2.12 tff(8261,plain,
% 1.86/2.12 (r(elem!1, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8260, 8253])).
% 1.86/2.12 tff(8262,plain,
% 1.86/2.12 (~r(z, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4164, 8261, 274])).
% 1.86/2.12 tff(8263,plain,
% 1.86/2.12 (b(z, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1786, 8262])).
% 1.86/2.12 tff(8264,plain,
% 1.86/2.12 (~b(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7799, 8263, 118, 173])).
% 1.86/2.12 tff(8265,plain,
% 1.86/2.12 (r(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[963, 8264])).
% 1.86/2.12 tff(8266,plain,
% 1.86/2.12 (~r(s(z), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2896, 8265, 274])).
% 1.86/2.12 tff(8267,plain,
% 1.86/2.12 (b(s(z), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[727, 8266, 2754])).
% 1.86/2.12 tff(8268,plain,
% 1.86/2.12 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2831, 8267, 173, 8263, 8172, 8168])).
% 1.86/2.12 tff(8269,plain,
% 1.86/2.12 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2268, 8268])).
% 1.86/2.12 tff(8270,plain,
% 1.86/2.12 (~r(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2849, 189, 8261, 8269])).
% 1.86/2.12 tff(8271,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1355, 189, 1339, 8269])).
% 1.86/2.12 tff(8272,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2854, 8271])).
% 1.86/2.12 tff(8273,plain,
% 1.86/2.12 (~b(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2866, 8272, 118, 173])).
% 1.86/2.12 tff(8274,plain,
% 1.86/2.12 (r(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2242, 8273])).
% 1.86/2.12 tff(8275,plain,
% 1.86/2.12 (~r(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2253, 8274, 173])).
% 1.86/2.12 tff(8276,plain,
% 1.86/2.12 (b(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2229, 8275])).
% 1.86/2.12 tff(8277,plain,
% 1.86/2.12 (~b(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4234, 337, 327, 8267, 8276])).
% 1.86/2.12 tff(8278,plain,
% 1.86/2.12 (s(s(z)) = elem!1),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2301, 8277, 8270])).
% 1.86/2.12 tff(8279,plain,
% 1.86/2.12 (s(s(s(z))) = s(elem!1)),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8278])).
% 1.86/2.12 tff(8280,plain,
% 1.86/2.12 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.12 tff(8281,plain,
% 1.86/2.12 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8280])).
% 1.86/2.12 tff(8282,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8281])).
% 1.86/2.12 tff(8283,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8282])).
% 1.86/2.12 tff(8284,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8168, 8283])).
% 1.86/2.12 tff(8285,plain,
% 1.86/2.12 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.12 tff(8286,plain,
% 1.86/2.12 (b(s(elem!1), z)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[1770, 8285])).
% 1.86/2.12 tff(8287,plain,
% 1.86/2.12 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.12 tff(8288,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8278])).
% 1.86/2.12 tff(8289,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3590, 189, 1339, 8269])).
% 1.86/2.12 tff(8290,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4268, 8289])).
% 1.86/2.12 tff(8291,plain,
% 1.86/2.12 (b(elem!1, s(s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8290, 8288])).
% 1.86/2.12 tff(8292,plain,
% 1.86/2.12 (b(elem!1, s(elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8291, 8287])).
% 1.86/2.12 tff(8293,plain,
% 1.86/2.12 (s(elem!1) = s(s(s(z)))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8279])).
% 1.86/2.12 tff(8294,plain,
% 1.86/2.12 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8293])).
% 1.86/2.12 tff(8295,plain,
% 1.86/2.12 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.86/2.12 inference(symmetry,[status(thm)],[8294])).
% 1.86/2.12 tff(8296,plain,
% 1.86/2.12 (b(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2463, 2461, 1481])).
% 1.86/2.12 tff(8297,plain,
% 1.86/2.12 (b(s(elem!1), elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8296, 8295])).
% 1.86/2.12 tff(8298,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8299,plain,
% 1.86/2.12 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~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(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8300,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8299])).
% 1.86/2.12 tff(8301,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8300, 8298])).
% 1.86/2.12 tff(8302,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8303,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8302, 8301])).
% 1.86/2.12 tff(8304,plain,
% 1.86/2.12 (~b(s(z), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8303, 337, 8297, 8267, 8292, 8286])).
% 1.86/2.12 tff(8305,plain,
% 1.86/2.12 (r(s(z), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2133, 43, 8304, 55])).
% 1.86/2.12 tff(8306,plain,
% 1.86/2.12 (~r(z, s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2578, 8267, 173, 327, 50, 274, 981])).
% 1.86/2.12 tff(8307,plain,
% 1.86/2.12 (b(z, s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[395, 8306])).
% 1.86/2.12 tff(8308,plain,
% 1.86/2.12 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1927, 8286, 1925, 8307])).
% 1.86/2.12 tff(8309,plain,
% 1.86/2.12 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[363, 8308, 172])).
% 1.86/2.12 tff(8310,plain,
% 1.86/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8311,plain,
% 1.86/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8312,plain,
% 1.86/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8311, 8310])).
% 1.86/2.12 tff(8313,plain,
% 1.86/2.12 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8312, 189, 8309, 8305])).
% 1.86/2.12 tff(8314,plain,
% 1.86/2.12 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[227, 43, 8313, 213])).
% 1.86/2.12 tff(8315,plain,
% 1.86/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8316,plain,
% 1.86/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8317,plain,
% 1.86/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8316, 8315])).
% 1.86/2.12 tff(8318,plain,
% 1.86/2.12 (~r(s(z), s(s(s(elem!1))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8317, 189, 8309, 8305])).
% 1.86/2.12 tff(8319,plain,
% 1.86/2.12 (b(s(z), s(s(s(elem!1))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1970, 8318])).
% 1.86/2.12 tff(8320,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8321,plain,
% 1.86/2.12 (((~b(s(s(s(elem!1))), s(z))) | (~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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8322,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8321])).
% 1.86/2.12 tff(8323,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8322, 8320])).
% 1.86/2.12 tff(8324,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8325,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8324, 8323])).
% 1.86/2.12 tff(8326,plain,
% 1.86/2.12 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8325, 337, 8319, 8314, 8284])).
% 1.86/2.12 tff(8327,plain,
% 1.86/2.12 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8281])).
% 1.86/2.12 tff(8328,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8327])).
% 1.86/2.12 tff(8329,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.12 tff(8330,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8329, 8328])).
% 1.86/2.12 tff(8331,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.12 tff(8332,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8331])).
% 1.86/2.12 tff(8333,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8281])).
% 1.86/2.12 tff(8334,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8333, 8332])).
% 1.86/2.12 tff(8335,plain,
% 1.86/2.12 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8334])).
% 1.86/2.12 tff(8336,plain,
% 1.86/2.12 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8281])).
% 1.86/2.12 tff(8337,plain,
% 1.86/2.12 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.86/2.12 inference(symmetry,[status(thm)],[8336])).
% 1.86/2.12 tff(8338,plain,
% 1.86/2.12 (b(z, s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8263, 8337])).
% 1.97/2.12 tff(8339,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8340,plain,
% 1.97/2.12 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8341,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[8340])).
% 1.97/2.12 tff(8342,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.12 inference(transitivity,[status(thm)],[8341, 8339])).
% 1.97/2.12 tff(8343,plain,
% 1.97/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(8344,plain,
% 1.97/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8343, 8342])).
% 1.97/2.12 tff(8345,plain,
% 1.97/2.12 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8344, 337, 327, 8307, 8297])).
% 1.97/2.12 tff(8346,plain,
% 1.97/2.12 (~b(s(s(elem!1)), s(elem!1))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8345, 8338, 8284])).
% 1.97/2.12 tff(8347,plain,
% 1.97/2.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8346, 8335])).
% 1.97/2.12 tff(8348,plain,
% 1.97/2.12 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[524, 8347])).
% 1.97/2.12 tff(8349,plain,
% 1.97/2.12 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8348, 8330])).
% 1.97/2.12 tff(8350,plain,
% 1.97/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8351,plain,
% 1.97/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(8352,plain,
% 1.97/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8351, 8350])).
% 1.97/2.12 tff(8353,plain,
% 1.97/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8352, 189, 8309, 8349])).
% 1.97/2.12 tff(8354,plain,
% 1.97/2.12 (((~![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)))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8355,plain,
% 1.97/2.12 ((~![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)))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(8356,plain,
% 1.97/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8355, 8354])).
% 1.97/2.12 tff(8357,plain,
% 1.97/2.12 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8356, 43, 8353, 8326])).
% 1.97/2.12 tff(8358,plain,
% 1.97/2.12 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.97/2.12 inference(transitivity,[status(thm)],[8280, 8357])).
% 1.97/2.12 tff(8359,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[4560, 8358])).
% 1.97/2.12 tff(8360,plain,(r(s(s(s(z))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (s(z) = elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8361,plain,
% 1.97/2.13 (r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8360, 172, 327, 2518, 7636, 173, 49, 1339, 50, 8246, 272, 7958])).
% 1.97/2.13 tff(8362,plain,
% 1.97/2.13 (~r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4123, 8361, 49])).
% 1.97/2.13 tff(8363,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[727, 8362, 272])).
% 1.97/2.13 tff(8364,plain,
% 1.97/2.13 (~r(z, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2578, 8363, 173, 327, 50, 8246, 981])).
% 1.97/2.13 tff(8365,plain,
% 1.97/2.13 (b(z, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[395, 8364])).
% 1.97/2.13 tff(8366,plain,
% 1.97/2.13 (s(s(s(s(z)))) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8174, 8361, 327, 1339, 49])).
% 1.97/2.13 tff(8367,plain,
% 1.97/2.13 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[801, 8366, 247])).
% 1.97/2.13 tff(8368,plain,
% 1.97/2.13 (~(s(s(s(z))) = s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2510, 8366, 50])).
% 1.97/2.13 tff(8369,plain,
% 1.97/2.13 (~b(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2594, 2520, 247, 1878, 1075])).
% 1.97/2.13 tff(8370,plain,
% 1.97/2.13 (r(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[898, 8369, 50])).
% 1.97/2.13 tff(8371,plain,
% 1.97/2.13 (~r(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2381, 189, 8370, 173])).
% 1.97/2.13 tff(8372,plain,
% 1.97/2.13 (b(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[378, 43, 114, 8371])).
% 1.97/2.13 tff(8373,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4845, 189, 8370, 118])).
% 1.97/2.13 tff(8374,plain,
% 1.97/2.13 (b(s(s(s(z))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 8373])).
% 1.97/2.13 tff(8375,plain,
% 1.97/2.13 ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5804, 337, 600, 2520, 1770])).
% 1.97/2.13 tff(8376,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8375, 8374, 8372])).
% 1.97/2.13 tff(8377,plain,((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8378,plain,
% 1.97/2.13 (~b(s(elem!1), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8377, 8365, 8368, 49, 173, 50, 247, 8362, 8247])).
% 1.97/2.13 tff(8379,plain,
% 1.97/2.13 (r(s(elem!1), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[270, 8378, 265])).
% 1.97/2.13 tff(8380,plain,
% 1.97/2.13 (~r(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8043, 8379, 7636, 173, 8367, 172, 327, 8363, 8365])).
% 1.97/2.13 tff(8381,plain,
% 1.97/2.13 (b(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[898, 8380, 50])).
% 1.97/2.13 tff(8382,plain,
% 1.97/2.13 (~b(elem!1, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1888, 8381, 327, 8363])).
% 1.97/2.13 tff(8383,plain,
% 1.97/2.13 (r(elem!1, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1015, 8382, 981])).
% 1.97/2.13 tff(8384,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8075, 8379, 8361, 172, 8366, 50, 247])).
% 1.97/2.13 tff(8385,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8386,plain,
% 1.97/2.13 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~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))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8387,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8386])).
% 1.97/2.13 tff(8388,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8387, 8385])).
% 1.97/2.13 tff(8389,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8390,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8389, 8388])).
% 1.97/2.13 tff(8391,plain,
% 1.97/2.13 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8390, 337, 8384, 8365, 8381, 8363, 7636])).
% 1.97/2.13 tff(8392,plain,
% 1.97/2.13 (r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[363, 8391, 172])).
% 1.97/2.13 tff(8393,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2483, 189, 8379, 8361])).
% 1.97/2.13 tff(8394,plain,
% 1.97/2.13 (b(z, elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8060, 8393, 8363, 50, 173, 8379, 172, 327, 3])).
% 1.97/2.13 tff(8395,plain,
% 1.97/2.13 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[358, 353, 273])).
% 1.97/2.13 tff(8396,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[350, 8395, 276])).
% 1.97/2.13 tff(8397,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[972, 8396, 327, 925])).
% 1.97/2.13 tff(8398,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8021, 353, 2543])).
% 1.97/2.13 tff(8399,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[295, 43, 8398, 282, 8397])).
% 1.97/2.13 tff(8400,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8401,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8400, 8394, 8392, 327, 8367, 8379, 8383])).
% 1.97/2.13 tff(8402,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(z))), s(z)) | (elem!1 = s(z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8403,plain,
% 1.97/2.13 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8402, 1339, 50, 173, 3, 247, 327])).
% 1.97/2.13 tff(8404,plain,
% 1.97/2.13 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[170, 8403, 50])).
% 1.97/2.13 tff(8405,plain,
% 1.97/2.13 (~r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8174, 8404, 327, 1339, 49])).
% 1.97/2.13 tff(8406,plain,
% 1.97/2.13 (b(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2463, 8405, 7958])).
% 1.97/2.13 tff(8407,plain,
% 1.97/2.13 (~(s(s(z)) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[155, 8403, 50])).
% 1.97/2.13 tff(8408,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7787, 1339, 49])).
% 1.97/2.13 tff(8409,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[851, 8408])).
% 1.97/2.13 tff(8410,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2027, 1339, 49])).
% 1.97/2.13 tff(8411,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1150, 8410])).
% 1.97/2.13 tff(8412,plain,
% 1.97/2.13 (~(elem!1 = s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2760, 8404])).
% 1.97/2.13 tff(8413,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8258, 337, 327, 8411, 8409])).
% 1.97/2.13 tff(8414,plain,
% 1.97/2.13 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2845, 43, 8413])).
% 1.97/2.13 tff(8415,plain,
% 1.97/2.13 (r(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8414, 8412])).
% 1.97/2.13 tff(8416,plain,
% 1.97/2.13 (~r(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4164, 8415, 8246])).
% 1.97/2.13 tff(8417,plain,
% 1.97/2.13 (b(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1786, 8416])).
% 1.97/2.13 tff(8418,plain,
% 1.97/2.13 (~b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7799, 8417, 49, 173])).
% 1.97/2.13 tff(8419,plain,
% 1.97/2.13 (r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[963, 8418])).
% 1.97/2.13 tff(8420,plain,
% 1.97/2.13 (~r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2896, 8419, 8246])).
% 1.97/2.13 tff(8421,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[727, 8420, 272])).
% 1.97/2.13 tff(8422,plain,
% 1.97/2.13 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2831, 8421, 173, 8417, 8411, 8409])).
% 1.97/2.13 tff(8423,plain,
% 1.97/2.13 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2268, 8422])).
% 1.97/2.13 tff(8424,plain,
% 1.97/2.13 (~r(s(s(z)), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2849, 189, 8415, 8423])).
% 1.97/2.13 tff(8425,plain,
% 1.97/2.13 (b(s(s(z)), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2301, 8424, 8407])).
% 1.97/2.13 tff(8426,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1355, 189, 1339, 8423])).
% 1.97/2.13 tff(8427,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2854, 8426])).
% 1.97/2.13 tff(8428,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(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(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8429,plain,
% 1.97/2.13 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8430,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8429])).
% 1.97/2.13 tff(8431,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8430, 8428])).
% 1.97/2.13 tff(8432,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8433,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8432, 8431])).
% 1.97/2.13 tff(8434,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8433, 337, 327, 8421, 8427, 8425, 8406])).
% 1.97/2.13 tff(8435,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8436,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8435, 247, 173, 50, 3, 327])).
% 1.97/2.13 tff(8437,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[548, 8436])).
% 1.97/2.13 tff(8438,plain,
% 1.97/2.13 (r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2463, 2460, 1481])).
% 1.97/2.13 tff(8439,plain,
% 1.97/2.13 (~r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4123, 8438, 118])).
% 1.97/2.13 tff(8440,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2031, 8439, 118, 173, 247, 1710])).
% 1.97/2.13 tff(8441,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[727, 8439, 272])).
% 1.97/2.13 tff(8442,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8224, 337, 327, 8441, 8188])).
% 1.97/2.13 tff(8443,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[857, 853, 229])).
% 1.97/2.13 tff(8444,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1177, 8443, 274])).
% 1.97/2.13 tff(8445,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1792, 8444])).
% 1.97/2.13 tff(8446,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.97/2.13 tff(8447,plain,
% 1.97/2.13 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2845, 43, 8446])).
% 1.97/2.13 tff(8448,plain,
% 1.97/2.13 (r(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8447, 4102])).
% 1.97/2.13 tff(8449,plain,
% 1.97/2.13 (~r(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4164, 8448, 274])).
% 1.97/2.13 tff(8450,plain,
% 1.97/2.13 (b(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1786, 8449])).
% 1.97/2.13 tff(8451,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1795, 8450, 8445, 1659, 2])).
% 1.97/2.13 tff(8452,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, z)) | b(elem!1, s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8453,plain,
% 1.97/2.13 (s(s(s(s(z)))) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8452, 8442, 2, 274, 1770, 8440])).
% 1.97/2.13 tff(8454,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8453])).
% 1.97/2.13 tff(8455,plain,
% 1.97/2.13 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[8454])).
% 1.97/2.13 tff(8456,plain,
% 1.97/2.13 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8455])).
% 1.97/2.13 tff(8457,plain,
% 1.97/2.13 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2460, 8456])).
% 1.97/2.13 tff(8458,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2, 8457])).
% 1.97/2.13 tff(8459,plain,(b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (elem!1 = s(z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8460,plain,
% 1.97/2.13 (b(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8459, 8437, 8246, 327, 49, 173, 247, 7958])).
% 1.97/2.13 tff(8461,plain,
% 1.97/2.13 (~r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2896, 1735, 274])).
% 1.97/2.13 tff(8462,plain,
% 1.97/2.13 (b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[963, 8461])).
% 1.97/2.13 tff(8463,plain,
% 1.97/2.13 (~r(z, elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1743, 1735, 173])).
% 1.97/2.13 tff(8464,plain,
% 1.97/2.13 (b(z, elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[921, 8463, 65])).
% 1.97/2.13 tff(8465,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3839, 337, 8464, 327, 8462, 1659, 2454, 7771])).
% 1.97/2.13 tff(8466,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (z = elem!1) | (~r(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8467,plain,
% 1.97/2.13 (~r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8466, 8460, 7963, 327, 7961, 61, 8246, 173])).
% 1.97/2.13 tff(8468,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2031, 8467, 49, 173, 247, 8247])).
% 1.97/2.13 tff(8469,plain,
% 1.97/2.13 (~r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8466, 2454, 1770, 327, 201, 61, 274, 173])).
% 1.97/2.13 tff(8470,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[727, 8469, 272])).
% 1.97/2.13 tff(8471,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2031, 8469, 118, 173, 247, 1710])).
% 1.97/2.13 tff(8472,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8224, 337, 327, 8470, 8188])).
% 1.97/2.13 tff(8473,plain,
% 1.97/2.13 (s(s(s(s(z)))) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8452, 8472, 2, 274, 1770, 8471])).
% 1.97/2.13 tff(8474,plain,
% 1.97/2.13 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[801, 8473, 247])).
% 1.97/2.13 tff(8475,plain,
% 1.97/2.13 (~r(z, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2578, 8470, 173, 327, 50, 274, 981])).
% 1.97/2.13 tff(8476,plain,
% 1.97/2.13 (b(z, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[395, 8475])).
% 1.97/2.13 tff(8477,plain,
% 1.97/2.13 (~(s(s(s(z))) = s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2510, 8473, 50])).
% 1.97/2.13 tff(8478,plain,
% 1.97/2.13 (~b(s(elem!1), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8377, 8477, 8476, 118, 173, 50, 247, 8469, 1710])).
% 1.97/2.13 tff(8479,plain,
% 1.97/2.13 (r(s(elem!1), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[270, 8478, 265])).
% 1.97/2.13 tff(8480,plain,
% 1.97/2.13 (~r(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5224, 8479, 274])).
% 1.97/2.13 tff(8481,plain,
% 1.97/2.13 (b(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[378, 43, 114, 8480])).
% 1.97/2.13 tff(8482,plain,
% 1.97/2.13 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1927, 8481, 1925, 8476])).
% 1.97/2.13 tff(8483,plain,
% 1.97/2.13 (r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[363, 8482, 172])).
% 1.97/2.13 tff(8484,plain,
% 1.97/2.13 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[358, 8483, 8479])).
% 1.97/2.13 tff(8485,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[350, 8484, 8474])).
% 1.97/2.13 tff(8486,plain,
% 1.97/2.13 (~r(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8043, 8479, 1925, 173, 8474, 172, 327, 8470, 8476])).
% 1.97/2.13 tff(8487,plain,
% 1.97/2.13 (b(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[898, 8486, 50])).
% 1.97/2.13 tff(8488,plain,
% 1.97/2.13 (~b(elem!1, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1888, 8487, 327, 8470])).
% 1.97/2.13 tff(8489,plain,
% 1.97/2.13 (r(elem!1, s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1015, 8488, 981])).
% 1.97/2.13 tff(8490,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[345, 8396, 327, 324])).
% 1.97/2.13 tff(8491,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[295, 43, 8398, 282, 8490])).
% 1.97/2.13 tff(8492,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8493,plain,
% 1.97/2.13 (~b(s(z), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8492, 8483, 327, 8474, 8479, 8489])).
% 1.97/2.13 tff(8494,plain,
% 1.97/2.13 (r(s(z), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1970, 8493])).
% 1.97/2.13 tff(8495,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5465, 8494, 8485, 2451, 327, 2454, 8470])).
% 1.97/2.13 tff(8496,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8497,plain,
% 1.97/2.13 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8496, 8460, 327, 7636, 50, 173, 8246, 49, 247, 8437])).
% 1.97/2.13 tff(8498,plain,
% 1.97/2.13 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[170, 8497, 50])).
% 1.97/2.13 tff(8499,plain,
% 1.97/2.13 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8452, 8498, 8437, 8246, 7963, 8468])).
% 1.97/2.13 tff(8500,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8180, 8437, 7963, 173])).
% 1.97/2.13 tff(8501,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[851, 8500])).
% 1.97/2.13 tff(8502,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[727, 8467, 272])).
% 1.97/2.13 tff(8503,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8224, 337, 327, 8502, 8501, 8499])).
% 1.97/2.13 tff(8504,plain,((elem!1 = s(z)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8505,plain,
% 1.97/2.13 (elem!1 = s(z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8504, 7956, 50, 81, 3])).
% 1.97/2.13 tff(8506,plain,
% 1.97/2.13 (s(z) = elem!1),
% 1.97/2.13 inference(symmetry,[status(thm)],[8505])).
% 1.97/2.13 tff(8507,plain,
% 1.97/2.13 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8506])).
% 1.97/2.13 tff(8508,plain,
% 1.97/2.13 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.97/2.13 inference(symmetry,[status(thm)],[8507])).
% 1.97/2.13 tff(8509,plain,
% 1.97/2.13 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8508])).
% 1.97/2.13 tff(8510,plain,
% 1.97/2.13 (~b(elem!1, s(z))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6600, 8509])).
% 1.97/2.13 tff(8511,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7956, 8510])).
% 1.97/2.13 tff(8512,plain,(b(z, s(z)) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8513,plain,
% 1.97/2.13 (b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8512, 50, 3])).
% 1.97/2.13 tff(8514,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.97/2.13 tff(8515,plain,
% 1.97/2.13 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.13 inference(symmetry,[status(thm)],[8514])).
% 1.97/2.13 tff(8516,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2470, 8515])).
% 1.97/2.13 tff(8517,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8518,plain,
% 1.97/2.13 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8517, 2451])).
% 1.97/2.13 tff(8519,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.97/2.13 tff(8520,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[851, 8519])).
% 1.97/2.13 tff(8521,plain,
% 1.97/2.13 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[245])).
% 1.97/2.13 tff(8522,plain,
% 1.97/2.13 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 1.97/2.13 inference(symmetry,[status(thm)],[8521])).
% 1.97/2.13 tff(8523,plain,
% 1.97/2.13 (~r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3927, 1474, 118])).
% 1.97/2.13 tff(8524,plain,
% 1.97/2.13 (b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[963, 8523])).
% 1.97/2.13 tff(8525,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8526,plain,
% 1.97/2.13 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8527,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8526])).
% 1.97/2.13 tff(8528,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8527, 8525])).
% 1.97/2.13 tff(8529,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8530,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8529, 8528])).
% 1.97/2.14 tff(8531,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8530, 337, 1925, 1, 1301, 241])).
% 1.97/2.14 tff(8532,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8533,plain,
% 1.97/2.14 (~b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8532, 8524, 1925, 1301])).
% 1.97/2.14 tff(8534,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[227, 43, 8533, 213])).
% 1.97/2.14 tff(8535,plain,
% 1.97/2.14 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6403, 189, 8534, 118])).
% 1.97/2.14 tff(8536,plain,
% 1.97/2.14 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6407, 43, 8535])).
% 1.97/2.14 tff(8537,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8536, 6383])).
% 1.97/2.14 tff(8538,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.97/2.14 tff(8539,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8540,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8541,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8540, 8539])).
% 1.97/2.14 tff(8542,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8541, 189, 811, 214])).
% 1.97/2.14 tff(8543,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1947, 43, 4560, 8542])).
% 1.97/2.14 tff(8544,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7787, 811, 118])).
% 1.97/2.14 tff(8545,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[548, 8544])).
% 1.97/2.14 tff(8546,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8547,plain,
% 1.97/2.14 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8548,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8547])).
% 1.97/2.14 tff(8549,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8548, 8546])).
% 1.97/2.14 tff(8550,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8551,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8550, 8549])).
% 1.97/2.14 tff(8552,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8551, 337, 4946, 8545, 8543, 8538])).
% 1.97/2.14 tff(8553,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8554,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8553, 2518, 8537, 118, 8534])).
% 1.97/2.14 tff(8555,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[851, 8554])).
% 1.97/2.14 tff(8556,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8557,plain,
% 1.97/2.14 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8558,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8557])).
% 1.97/2.14 tff(8559,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8558, 8556])).
% 1.97/2.14 tff(8560,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8561,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 1.97/2.14 tff(8562,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8561, 337, 1925, 8524, 1301, 8555])).
% 1.97/2.14 tff(8563,plain,
% 1.97/2.14 (r(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1792, 8562])).
% 1.97/2.14 tff(8564,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7557, 189, 1474, 8563])).
% 1.97/2.14 tff(8565,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[524, 8564])).
% 1.97/2.14 tff(8566,plain,
% 1.97/2.14 (~b(z, s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4738, 337, 8524, 1301, 8555])).
% 1.97/2.14 tff(8567,plain,
% 1.97/2.14 (r(z, s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1786, 8566])).
% 1.97/2.14 tff(8568,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5075, 8567, 1474])).
% 1.97/2.14 tff(8569,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[548, 8568])).
% 1.97/2.14 tff(8570,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8571,plain,
% 1.97/2.14 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8572,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8571])).
% 1.97/2.14 tff(8573,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8572, 8570])).
% 1.97/2.14 tff(8574,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8575,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8574, 8573])).
% 1.97/2.14 tff(8576,plain,
% 1.97/2.14 (~b(s(s(z)), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8575, 337, 1925, 1, 1301, 3357])).
% 1.97/2.14 tff(8577,plain,
% 1.97/2.14 (r(s(s(z)), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2242, 8576])).
% 1.97/2.14 tff(8578,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(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(X1, 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)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8579,plain,
% 1.97/2.14 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8580,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8579])).
% 1.97/2.14 tff(8581,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8580, 8578])).
% 1.97/2.14 tff(8582,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8583,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8582, 8581])).
% 1.97/2.14 tff(8584,plain,
% 1.97/2.14 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8583, 337, 1, 1301, 1231, 3357])).
% 1.97/2.14 tff(8585,plain,
% 1.97/2.14 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2268, 8584])).
% 1.97/2.14 tff(8586,plain,
% 1.97/2.14 (~b(z, s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4738, 337, 1, 1301, 1231])).
% 1.97/2.14 tff(8587,plain,
% 1.97/2.14 (r(z, s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1786, 8586])).
% 1.97/2.14 tff(8588,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4338, 189, 8587, 8585, 8577])).
% 1.97/2.14 tff(8589,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8590,plain,
% 1.97/2.14 (~b(s(s(z)), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8589, 8555, 1301, 8524, 1925])).
% 1.97/2.14 tff(8591,plain,
% 1.97/2.14 (r(s(s(z)), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2229, 8590])).
% 1.97/2.14 tff(8592,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8593,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8594,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8593, 8592])).
% 1.97/2.14 tff(8595,plain,
% 1.97/2.14 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8594, 189, 214, 2245])).
% 1.97/2.14 tff(8596,assumption,(~(s(s(z)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.97/2.14 tff(8597,plain,
% 1.97/2.14 (b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2317, 43, 8596, 8595])).
% 1.97/2.14 tff(8598,plain,
% 1.97/2.14 (~r(s(s(z)), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1293, 189, 118, 2245])).
% 1.97/2.14 tff(8599,plain,
% 1.97/2.14 (b(s(s(z)), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4268, 8598])).
% 1.97/2.14 tff(8600,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), 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(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8601,plain,
% 1.97/2.14 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~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(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8602,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), 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(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8601])).
% 1.97/2.14 tff(8603,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), 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(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8602, 8600])).
% 1.97/2.14 tff(8604,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8605,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8604, 8603])).
% 1.97/2.14 tff(8606,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8605, 337, 3243, 2, 8599, 8538, 8597])).
% 1.97/2.14 tff(8607,plain,((~r(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(s(elem!1))), s(s(s(z))))) | (s(s(z)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8608,plain,
% 1.97/2.14 (s(s(z)) = s(s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8607, 8591, 8569, 8537, 8565, 118, 8534])).
% 1.97/2.14 tff(8609,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.97/2.14 tff(8610,plain,
% 1.97/2.14 (s(elem!1) = s(s(s(s(z))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8609])).
% 1.97/2.14 tff(8611,plain,
% 1.97/2.14 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8610])).
% 1.97/2.14 tff(8612,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.97/2.14 tff(8613,plain,
% 1.97/2.14 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8612])).
% 1.97/2.14 tff(8614,plain,
% 1.97/2.14 (s(z) = s(s(s(s(s(z)))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[105, 8613, 87, 8611])).
% 1.97/2.14 tff(8615,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2331, 8614])).
% 1.97/2.14 tff(8616,plain,((~(s(s(z)) = s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8617,plain,
% 1.97/2.14 (~(elem!1 = s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8616, 8608])).
% 1.97/2.14 tff(8618,plain,
% 1.97/2.14 (~r(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3916, 189, 4406, 118])).
% 1.97/2.14 tff(8619,plain,
% 1.97/2.14 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5966, 43, 8618])).
% 1.97/2.14 tff(8620,plain,
% 1.97/2.14 (b(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8619, 8617])).
% 1.97/2.14 tff(8621,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8622,plain,
% 1.97/2.14 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8623,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, 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(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8622])).
% 1.97/2.15 tff(8624,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, 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(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8623, 8621])).
% 1.97/2.15 tff(8625,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8626,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8625, 8624])).
% 1.97/2.15 tff(8627,plain,
% 1.97/2.15 (~b(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8626, 337, 8565, 8569, 8537, 8620])).
% 1.97/2.15 tff(8628,plain,
% 1.97/2.15 (~r(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6420, 189, 4406, 8534])).
% 1.97/2.15 tff(8629,plain,
% 1.97/2.15 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[295, 43, 8628])).
% 1.97/2.15 tff(8630,plain,
% 1.97/2.15 (elem!1 = s(s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8629, 8627])).
% 1.97/2.15 tff(8631,plain,
% 1.97/2.15 (s(s(s(elem!1))) = elem!1),
% 1.97/2.15 inference(symmetry,[status(thm)],[8630])).
% 1.97/2.15 tff(8632,plain,
% 1.97/2.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8631])).
% 1.97/2.15 tff(8633,plain,
% 1.97/2.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8632, 2114])).
% 1.97/2.15 tff(8634,plain,
% 1.97/2.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 1.97/2.15 inference(transitivity,[status(thm)],[8633, 2115])).
% 1.97/2.15 tff(8635,plain,
% 1.97/2.15 (s(s(z)) = elem!1),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8608, 8634])).
% 1.97/2.15 tff(8636,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[157])).
% 1.97/2.15 tff(8637,plain,
% 1.97/2.15 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[8636])).
% 1.97/2.15 tff(8638,plain,
% 1.97/2.15 ((~b(elem!1, s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8637])).
% 1.97/2.15 tff(8639,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4370, 8638])).
% 1.97/2.15 tff(8640,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1231, 8639])).
% 1.97/2.15 tff(8641,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(z)))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8642,plain,
% 1.97/2.15 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8641, 8555, 4370])).
% 1.97/2.15 tff(8643,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8644,plain,
% 1.97/2.15 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~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)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8645,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8644])).
% 1.97/2.15 tff(8646,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8645, 8643])).
% 1.97/2.15 tff(8647,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8648,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8647, 8646])).
% 1.97/2.15 tff(8649,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8648, 337, 8565, 8569, 8620])).
% 1.97/2.15 tff(8650,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[857, 8649, 8642])).
% 1.97/2.15 tff(8651,plain,
% 1.97/2.15 (~r(elem!1, z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1177, 8650, 8563])).
% 1.97/2.15 tff(8652,plain,
% 1.97/2.15 (b(elem!1, z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1759, 8651, 68])).
% 1.97/2.15 tff(8653,plain,
% 1.97/2.15 (~r(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3923, 189, 4406, 118])).
% 1.97/2.15 tff(8654,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8551, 337, 8565, 8569, 8537])).
% 1.97/2.15 tff(8655,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1947, 43, 2518, 8654])).
% 1.97/2.15 tff(8656,plain,
% 1.97/2.15 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2153, 4406, 8534])).
% 1.97/2.15 tff(8657,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8658,plain,
% 1.97/2.15 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8659,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), 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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8658])).
% 1.97/2.15 tff(8660,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), 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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8659, 8657])).
% 1.97/2.15 tff(8661,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8662,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8661, 8660])).
% 1.97/2.15 tff(8663,plain,
% 1.97/2.15 (~b(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8662, 337, 8565, 8569, 8537, 8620])).
% 1.97/2.15 tff(8664,plain,
% 1.97/2.15 (s(s(s(elem!1))) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[350, 8663, 8656])).
% 1.97/2.15 tff(8665,plain,
% 1.97/2.15 (b(z, elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7903, 8664, 1925])).
% 1.97/2.15 tff(8666,plain,
% 1.97/2.15 (~b(s(z), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4005, 8652, 1301, 8665])).
% 1.97/2.15 tff(8667,plain,
% 1.97/2.15 (r(s(z), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[727, 8666, 272])).
% 1.97/2.15 tff(8668,plain,
% 1.97/2.15 (~b(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8532, 1, 1925, 1301])).
% 1.97/2.15 tff(8669,plain,
% 1.97/2.15 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[227, 43, 8668, 213])).
% 1.97/2.15 tff(8670,plain,
% 1.97/2.15 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2153, 777, 8669])).
% 1.97/2.15 tff(8671,plain,
% 1.97/2.15 (b(s(elem!1), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[270, 265, 3062])).
% 1.97/2.15 tff(8672,plain,
% 1.97/2.15 (~b(s(s(s(elem!1))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3647, 326, 1763, 1925])).
% 1.97/2.15 tff(8673,plain,
% 1.97/2.15 (r(s(s(s(elem!1))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[406, 43, 133, 8672])).
% 1.97/2.15 tff(8674,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8675,plain,
% 1.97/2.15 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8676,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8675])).
% 1.97/2.15 tff(8677,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8676, 8674])).
% 1.97/2.15 tff(8678,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8679,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8678, 8677])).
% 1.97/2.15 tff(8680,plain,
% 1.97/2.15 (~b(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8679, 337, 1763, 326, 1925, 1, 1301])).
% 1.97/2.15 tff(8681,plain,
% 1.97/2.15 (r(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[310, 43, 211, 8680])).
% 1.97/2.15 tff(8682,plain,
% 1.97/2.15 (~r(z, s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3167, 353, 2177])).
% 1.97/2.15 tff(8683,plain,
% 1.97/2.15 (b(z, s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[395, 8682])).
% 1.97/2.15 tff(8684,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8685,plain,
% 1.97/2.15 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8686,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8685])).
% 1.97/2.15 tff(8687,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8686, 8684])).
% 1.97/2.15 tff(8688,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8689,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8688, 8687])).
% 1.97/2.15 tff(8690,plain,
% 1.97/2.15 (~b(s(z), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8689, 337, 1763, 8683, 2520, 1, 1301])).
% 1.97/2.15 tff(8691,plain,
% 1.97/2.15 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2133, 43, 8690])).
% 1.97/2.15 tff(8692,plain,
% 1.97/2.15 (r(s(z), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8691, 4012])).
% 1.97/2.15 tff(8693,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8317, 189, 353, 298, 8692])).
% 1.97/2.15 tff(8694,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8695,plain,
% 1.97/2.15 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8694, 8681, 50, 1763, 8671, 1, 1301, 8673])).
% 1.97/2.15 tff(8696,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[363, 8695, 172])).
% 1.97/2.15 tff(8697,plain,
% 1.97/2.15 (~b(s(elem!1), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6243, 8696, 1763, 326, 8671, 1301])).
% 1.97/2.15 tff(8698,plain,
% 1.97/2.15 (r(s(elem!1), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[898, 8697, 50])).
% 1.97/2.15 tff(8699,plain,
% 1.97/2.15 (r(elem!1, s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3157, 8696, 265, 326, 3062])).
% 1.97/2.15 tff(8700,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4434, 189, 8699, 777, 8698])).
% 1.97/2.15 tff(8701,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, z)) | (~b(z, s(z))) | r(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8702,plain,
% 1.97/2.15 (~b(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8701, 3062, 50, 1925, 1301, 1763, 172, 1, 777])).
% 1.97/2.15 tff(8703,plain,
% 1.97/2.15 (s(s(s(elem!1))) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[350, 8702, 8670])).
% 1.97/2.15 tff(8704,plain,
% 1.97/2.15 (~(s(s(s(z))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7671, 8703, 2451])).
% 1.97/2.15 tff(8705,plain,
% 1.97/2.15 (b(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2463, 8704, 2461])).
% 1.97/2.15 tff(8706,plain,
% 1.97/2.15 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7903, 6583, 1925])).
% 1.97/2.15 tff(8707,plain,
% 1.97/2.15 (r(z, elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[921, 6583, 65])).
% 1.97/2.15 tff(8708,plain,
% 1.97/2.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8709,plain,
% 1.97/2.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8710,plain,
% 1.97/2.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8709, 8708])).
% 1.97/2.15 tff(8711,plain,
% 1.97/2.15 (~r(s(s(s(elem!1))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8710, 189, 370, 352])).
% 1.97/2.15 tff(8712,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[406, 43, 133, 8711])).
% 1.97/2.15 tff(8713,plain,
% 1.97/2.15 (~r(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2164, 189, 352, 1735])).
% 1.97/2.15 tff(8714,plain,
% 1.97/2.15 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[310, 43, 211, 8713])).
% 1.97/2.15 tff(8715,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8716,plain,
% 1.97/2.15 (((~b(z, s(s(s(elem!1))))) | (~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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8717,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8716])).
% 1.97/2.15 tff(8718,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8717, 8715])).
% 1.97/2.16 tff(8719,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8720,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8719, 8718])).
% 1.97/2.16 tff(8721,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8720, 337, 1925, 4111, 8714, 8712])).
% 1.97/2.16 tff(8722,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8723,plain,
% 1.97/2.16 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8722, 8707, 1735, 1925])).
% 1.97/2.16 tff(8724,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[350, 8723, 8706, 984])).
% 1.97/2.16 tff(8725,plain,(b(z, elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8726,plain,
% 1.97/2.16 (b(z, elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8725, 8702, 1925, 1735, 61])).
% 1.97/2.16 tff(8727,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8728,plain,
% 1.97/2.16 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8729,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8728])).
% 1.97/2.16 tff(8730,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8729, 8727])).
% 1.97/2.16 tff(8731,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8732,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8731, 8730])).
% 1.97/2.16 tff(8733,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8732, 337, 8726, 1763, 3079, 8705])).
% 1.97/2.16 tff(8734,plain,
% 1.97/2.16 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8703])).
% 1.97/2.16 tff(8735,plain,
% 1.97/2.16 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8734])).
% 1.97/2.16 tff(8736,plain,
% 1.97/2.16 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8735])).
% 1.97/2.16 tff(8737,plain,
% 1.97/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8736])).
% 1.97/2.16 tff(8738,plain,
% 1.97/2.16 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8737])).
% 1.97/2.16 tff(8739,plain,
% 1.97/2.16 (~(s(s(s(z))) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[116, 8738])).
% 1.97/2.16 tff(8740,plain,
% 1.97/2.16 (r(s(s(s(z))), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4678, 43, 8739, 8733])).
% 1.97/2.16 tff(8741,plain,
% 1.97/2.16 (~b(s(elem!1), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3968, 337, 8726, 1763, 3079])).
% 1.97/2.16 tff(8742,plain,
% 1.97/2.16 (r(s(elem!1), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[378, 43, 114, 8741])).
% 1.97/2.16 tff(8743,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8744,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8745,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8744, 8743])).
% 1.97/2.16 tff(8746,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8745, 189, 8742, 1474, 8740])).
% 1.97/2.16 tff(8747,plain,(r(s(elem!1), elem!1) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | r(s(s(s(z))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8748,plain,
% 1.97/2.16 (r(s(elem!1), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8747, 1763, 1474, 2461, 1925, 1735, 50, 1301, 172, 1, 777])).
% 1.97/2.16 tff(8749,plain,
% 1.97/2.16 (~r(s(elem!1), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2099, 8748, 1735])).
% 1.97/2.16 tff(8750,plain,
% 1.97/2.16 (b(s(elem!1), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[898, 8749, 50])).
% 1.97/2.16 tff(8751,plain,
% 1.97/2.16 (~r(z, elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6190, 8748, 50, 1301, 1735])).
% 1.97/2.16 tff(8752,plain,
% 1.97/2.16 (b(z, elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[921, 8751, 61])).
% 1.97/2.16 tff(8753,plain,
% 1.97/2.16 (~b(s(s(s(elem!1))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7655, 8752, 1763, 1925])).
% 1.97/2.16 tff(8754,plain,
% 1.97/2.16 (s(s(s(elem!1))) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[350, 8753, 8670])).
% 1.97/2.16 tff(8755,plain,
% 1.97/2.16 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8754])).
% 1.97/2.16 tff(8756,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.97/2.16 tff(8757,plain,
% 1.97/2.16 (r(s(s(s(s(z)))), elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8756, 8755])).
% 1.97/2.16 tff(8758,plain,
% 1.97/2.16 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8754])).
% 1.97/2.16 tff(8759,plain,
% 1.97/2.16 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8758])).
% 1.97/2.16 tff(8760,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8759])).
% 1.97/2.16 tff(8761,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8760])).
% 1.97/2.16 tff(8762,plain,
% 1.97/2.16 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8761])).
% 1.97/2.16 tff(8763,plain,
% 1.97/2.16 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1466, 8754, 50])).
% 1.97/2.16 tff(8764,plain,
% 1.97/2.16 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8763, 8762])).
% 1.97/2.16 tff(8765,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5264, 8764, 8757, 1301, 1, 1735, 8748, 8750])).
% 1.97/2.16 tff(8766,plain,((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | r(s(s(s(z))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8767,plain,
% 1.97/2.16 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8766, 8667, 8524, 1301, 8655, 50, 1925, 1474, 8653, 8652, 4406])).
% 1.97/2.16 tff(8768,plain,
% 1.97/2.16 (~(s(s(z)) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[155, 8767, 50])).
% 1.97/2.16 tff(8769,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8768, 8635])).
% 1.97/2.16 tff(8770,plain,((elem!1 = s(z)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8771,plain,
% 1.97/2.16 (elem!1 = s(z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8770, 1474, 1301, 1925, 50, 118, 4370])).
% 1.97/2.16 tff(8772,plain,
% 1.97/2.16 (s(elem!1) = s(s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8771])).
% 1.97/2.16 tff(8773,plain,
% 1.97/2.16 (s(s(elem!1)) = s(s(s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8772])).
% 1.97/2.16 tff(8774,plain,
% 1.97/2.16 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8773])).
% 1.97/2.16 tff(8775,plain,
% 1.97/2.16 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8774])).
% 1.97/2.16 tff(8776,plain,
% 1.97/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8775])).
% 1.97/2.16 tff(8777,plain,
% 1.97/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8776, 6663])).
% 1.97/2.16 tff(8778,plain,
% 1.97/2.16 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8777])).
% 1.97/2.16 tff(8779,plain,
% 1.97/2.16 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[116, 8778])).
% 1.97/2.16 tff(8780,plain,
% 1.97/2.16 (s(z) = elem!1),
% 1.97/2.16 inference(symmetry,[status(thm)],[8771])).
% 1.97/2.16 tff(8781,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8780])).
% 1.97/2.16 tff(8782,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8781])).
% 1.97/2.16 tff(8783,plain,
% 1.97/2.16 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8775])).
% 1.97/2.16 tff(8784,plain,
% 1.97/2.16 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8771])).
% 1.97/2.16 tff(8785,plain,
% 1.97/2.16 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8784, 6078])).
% 1.97/2.16 tff(8786,plain,
% 1.97/2.16 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8785])).
% 1.97/2.16 tff(8787,plain,
% 1.97/2.16 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[8786, 6671])).
% 1.97/2.16 tff(8788,plain,
% 1.97/2.16 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8787])).
% 1.97/2.16 tff(8789,plain,
% 1.97/2.16 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[135, 8788])).
% 1.97/2.16 tff(8790,plain,
% 1.97/2.16 (b(elem!1, z) <=> b(s(z), z)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8771])).
% 1.97/2.16 tff(8791,plain,
% 1.97/2.16 (b(s(z), z) <=> b(elem!1, z)),
% 1.97/2.16 inference(symmetry,[status(thm)],[8790])).
% 1.97/2.16 tff(8792,plain,
% 1.97/2.16 (b(elem!1, z)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8524, 8791])).
% 1.97/2.16 tff(8793,plain,
% 1.97/2.16 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8771])).
% 1.97/2.16 tff(8794,plain,
% 1.97/2.16 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.97/2.16 inference(symmetry,[status(thm)],[8793])).
% 1.97/2.16 tff(8795,plain,
% 1.97/2.16 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8772])).
% 1.97/2.16 tff(8796,plain,
% 1.97/2.16 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8795])).
% 1.97/2.16 tff(8797,plain,
% 1.97/2.16 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[8796, 8794])).
% 1.97/2.16 tff(8798,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8774])).
% 1.97/2.16 tff(8799,plain,
% 1.97/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8537, 8798])).
% 1.97/2.16 tff(8800,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8774])).
% 1.97/2.16 tff(8801,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6412, 189, 8534, 118])).
% 1.97/2.16 tff(8802,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2473, 43, 2451, 8801])).
% 1.97/2.16 tff(8803,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8802, 8800])).
% 1.97/2.16 tff(8804,plain,
% 1.97/2.16 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8774])).
% 1.97/2.16 tff(8805,plain,
% 1.97/2.16 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8804])).
% 1.97/2.16 tff(8806,plain,
% 1.97/2.16 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = s(s(s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8805])).
% 1.97/2.16 tff(8807,plain,
% 1.97/2.16 (~(s(s(z)) = s(s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[2263, 8806])).
% 1.97/2.16 tff(8808,plain,
% 1.97/2.16 (~r(s(s(z)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8607, 8807, 8803, 8537, 8799, 118, 8534])).
% 1.97/2.16 tff(8809,plain,
% 1.97/2.16 (b(s(s(z)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2229, 8808])).
% 1.97/2.16 tff(8810,plain,
% 1.97/2.16 (b(s(elem!1), elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8809, 8797])).
% 1.97/2.16 tff(8811,plain,
% 1.97/2.16 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8771])).
% 1.97/2.16 tff(8812,plain,
% 1.97/2.16 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8811])).
% 1.97/2.16 tff(8813,plain,
% 1.97/2.16 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8812])).
% 1.97/2.16 tff(8814,plain,
% 1.97/2.16 (~(elem!1 = s(s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[211, 8813])).
% 1.97/2.16 tff(8815,plain,
% 1.97/2.16 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[632, 8814])).
% 1.97/2.16 tff(8816,plain,
% 1.97/2.16 (b(z, elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6585, 8771, 1301])).
% 1.97/2.16 tff(8817,plain,
% 1.97/2.16 (b(s(elem!1), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8809, 8796])).
% 1.97/2.16 tff(8818,plain,
% 1.97/2.16 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8819,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8818])).
% 1.97/2.16 tff(8820,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8819, 5314])).
% 1.97/2.16 tff(8821,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8822,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8821, 8820])).
% 1.97/2.16 tff(8823,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8822, 337, 1544, 1, 1301, 599])).
% 1.97/2.16 tff(8824,plain,((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8825,plain,
% 1.97/2.16 (~b(s(elem!1), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8824, 8817, 1301, 8524])).
% 1.97/2.16 tff(8826,plain,
% 1.97/2.16 (r(s(elem!1), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1262, 8825, 8771])).
% 1.97/2.16 tff(8827,plain,
% 1.97/2.16 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4470, 8826, 8816, 8815, 8810, 8792])).
% 1.97/2.16 tff(8828,plain,
% 1.97/2.16 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[714, 8827, 8789])).
% 1.97/2.16 tff(8829,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8828, 8783])).
% 1.97/2.16 tff(8830,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8829, 8782])).
% 1.97/2.16 tff(8831,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6704, 8830])).
% 1.97/2.16 tff(8832,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6709, 8831, 8779])).
% 1.97/2.16 tff(8833,plain,
% 1.97/2.16 (~b(s(s(z)), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6693, 337, 8524, 1301, 8809])).
% 1.97/2.16 tff(8834,plain,
% 1.97/2.16 (r(s(s(z)), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2242, 8833])).
% 1.97/2.16 tff(8835,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8836,plain,
% 1.97/2.16 (((~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(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8837,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8836])).
% 1.97/2.16 tff(8838,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8837, 8835])).
% 1.97/2.16 tff(8839,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8840,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8839, 8838])).
% 1.97/2.16 tff(8841,plain,
% 1.97/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8840, 189, 1474, 8834])).
% 1.97/2.16 tff(8842,plain,
% 1.97/2.16 (b(s(s(z)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4268, 8841])).
% 1.97/2.16 tff(8843,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8844,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8845,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8844, 8843])).
% 1.97/2.16 tff(8846,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8845, 189, 1474, 8834])).
% 1.97/2.16 tff(8847,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2854, 8846])).
% 1.97/2.16 tff(8848,plain,
% 1.97/2.16 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7881, 8771])).
% 1.97/2.16 tff(8849,plain,
% 1.97/2.16 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8774])).
% 1.97/2.16 tff(8850,plain,
% 1.97/2.16 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8534, 8849])).
% 1.97/2.16 tff(8851,plain,
% 1.97/2.16 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6720, 189, 8850])).
% 1.97/2.16 tff(8852,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8851, 8830])).
% 1.97/2.16 tff(8853,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6726, 8852, 8848])).
% 1.97/2.16 tff(8854,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))), 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(X1, 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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8855,plain,
% 1.97/2.16 (((~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)))) | (~b(s(s(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(s(s(z))))))) <=> ((~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8856,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, 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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8855])).
% 1.97/2.17 tff(8857,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, 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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8856, 8854])).
% 1.97/2.17 tff(8858,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8859,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8858, 8857])).
% 1.97/2.17 tff(8860,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8859, 337, 8799, 8853, 8847, 8842, 8832])).
% 1.97/2.17 tff(8861,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8862,plain,
% 1.97/2.17 (~r(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8861, 4370, 1301, 1925, 50, 118])).
% 1.97/2.17 tff(8863,plain,
% 1.97/2.17 (b(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1498, 8862])).
% 1.97/2.17 tff(8864,plain,
% 1.97/2.17 (b(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3403, 445, 1925])).
% 1.97/2.17 tff(8865,plain,
% 1.97/2.17 (~b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4313, 8864, 1301, 8863, 8520])).
% 1.97/2.17 tff(8866,plain,
% 1.97/2.17 (r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[963, 6683])).
% 1.97/2.17 tff(8867,plain,
% 1.97/2.17 (~r(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3859, 4406, 275])).
% 1.97/2.17 tff(8868,plain,
% 1.97/2.17 (b(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1759, 8867, 68])).
% 1.97/2.17 tff(8869,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4963, 189, 4406, 811])).
% 1.97/2.17 tff(8870,plain,
% 1.97/2.17 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4730, 4406, 811])).
% 1.97/2.17 tff(8871,plain,
% 1.97/2.17 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2845, 43, 4102, 8870])).
% 1.97/2.17 tff(8872,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[857, 8869, 853])).
% 1.97/2.17 tff(8873,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8874,plain,
% 1.97/2.17 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8875,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8874])).
% 1.97/2.17 tff(8876,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8875, 8873])).
% 1.97/2.17 tff(8877,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8878,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8877, 8876])).
% 1.97/2.17 tff(8879,plain,
% 1.97/2.17 (~b(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8878, 337, 8868, 8545, 8872, 8871])).
% 1.97/2.17 tff(8880,plain,
% 1.97/2.17 (s(s(s(z))) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2463, 8879, 8653])).
% 1.97/2.17 tff(8881,plain,
% 1.97/2.17 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1472, 8880])).
% 1.97/2.17 tff(8882,plain,
% 1.97/2.17 (~r(s(elem!1), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[809, 8881, 8869])).
% 1.97/2.17 tff(8883,plain,
% 1.97/2.17 (b(s(elem!1), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[270, 8882, 978])).
% 1.97/2.17 tff(8884,plain,
% 1.97/2.17 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8880])).
% 1.97/2.17 tff(8885,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8884])).
% 1.97/2.17 tff(8886,plain,
% 1.97/2.17 (r(s(elem!1), s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[811, 8885])).
% 1.97/2.17 tff(8887,plain,
% 1.97/2.17 (~r(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3855, 275, 1735])).
% 1.97/2.17 tff(8888,plain,
% 1.97/2.17 (b(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[921, 8887, 65])).
% 1.97/2.17 tff(8889,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8890,plain,
% 1.97/2.17 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8891,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8890])).
% 1.97/2.17 tff(8892,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8891, 8889])).
% 1.97/2.17 tff(8893,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8894,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8893, 8892])).
% 1.97/2.17 tff(8895,plain,
% 1.97/2.17 ((~b(s(elem!1), z)) | (~b(z, elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8894, 337, 1763, 2520, 1925])).
% 1.97/2.17 tff(8896,plain,
% 1.97/2.17 (~b(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8895, 8888])).
% 1.97/2.17 tff(8897,plain,
% 1.97/2.17 (r(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[378, 43, 114, 8896])).
% 1.97/2.17 tff(8898,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4024, 189, 8897, 788, 275])).
% 1.97/2.17 tff(8899,plain,((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8900,plain,
% 1.97/2.17 (~r(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8899, 8886, 1925, 275, 8868, 61, 8883])).
% 1.97/2.17 tff(8901,plain,
% 1.97/2.17 (b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[727, 8900, 272])).
% 1.97/2.17 tff(8902,plain,
% 1.97/2.17 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8884])).
% 1.97/2.17 tff(8903,plain,
% 1.97/2.17 (b(elem!1, s(elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8871, 8902])).
% 1.97/2.17 tff(8904,plain,
% 1.97/2.17 (~b(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6311, 8903, 8868, 8883])).
% 1.97/2.17 tff(8905,plain,
% 1.97/2.17 (r(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[395, 8904])).
% 1.97/2.17 tff(8906,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6233, 8905, 8901, 1301, 8886, 50, 8883, 3146, 8868, 247])).
% 1.97/2.17 tff(8907,plain,((elem!1 = s(z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8908,plain,
% 1.97/2.17 (elem!1 = s(z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8907, 853, 50, 1925, 8866, 8520, 978, 1301, 118, 4370])).
% 1.97/2.17 tff(8909,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8908])).
% 1.97/2.17 tff(8910,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(symmetry,[status(thm)],[8909])).
% 1.97/2.17 tff(8911,plain,
% 1.97/2.17 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8910])).
% 1.97/2.17 tff(8912,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8519, 8911])).
% 1.97/2.17 tff(8913,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7787, 8520, 118])).
% 1.97/2.17 tff(8914,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[548, 8913])).
% 1.97/2.17 tff(8915,plain,
% 1.97/2.17 (b(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3403, 8908, 1925])).
% 1.97/2.17 tff(8916,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1795, 8915, 8863, 8914])).
% 1.97/2.17 tff(8917,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1792, 8916])).
% 1.97/2.17 tff(8918,plain,
% 1.97/2.17 (~b(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6686, 8908, 6683])).
% 1.97/2.17 tff(8919,plain,
% 1.97/2.17 (r(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1759, 8918, 68])).
% 1.97/2.17 tff(8920,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1177, 8919, 8917])).
% 1.97/2.17 tff(8921,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[857, 8920, 853])).
% 1.97/2.17 tff(8922,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8921, 8912])).
% 1.97/2.17 tff(8923,plain,((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), s(z)) | b(s(z), z) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8924,plain,
% 1.97/2.17 (s(elem!1) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8923, 8865, 853, 1925, 50, 8519, 1301, 118, 4370])).
% 1.97/2.17 tff(8925,plain,
% 1.97/2.17 (s(elem!1) = s(z)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8924, 8522])).
% 1.97/2.17 tff(8926,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[50, 8925])).
% 1.97/2.17 tff(8927,plain,((~(s(z) = elem!1)) | (s(elem!1) = s(z)) | (s(s(s(s(z)))) = elem!1) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8928,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8927, 8519, 853, 1925, 50, 1301, 118, 4370])).
% 1.97/2.17 tff(8929,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8928, 729])).
% 1.97/2.17 tff(8930,plain,
% 1.97/2.17 (r(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[322, 8929, 4370])).
% 1.97/2.17 tff(8931,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4963, 189, 8930, 8520])).
% 1.97/2.17 tff(8932,plain,
% 1.97/2.17 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4730, 8930, 8520])).
% 1.97/2.17 tff(8933,plain,
% 1.97/2.17 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2845, 43, 4102, 8932])).
% 1.97/2.17 tff(8934,plain,
% 1.97/2.17 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5069, 8933, 8520, 8930, 118])).
% 1.97/2.17 tff(8935,plain,
% 1.97/2.17 (~(s(elem!1) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[264, 8934])).
% 1.97/2.17 tff(8936,plain,
% 1.97/2.17 (s(s(s(s(z)))) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8923, 6683, 8519, 1925, 50, 978, 1301, 118, 4370])).
% 1.97/2.17 tff(8937,plain,
% 1.97/2.17 (elem!1 = s(s(s(s(z))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[8936])).
% 1.97/2.17 tff(8938,plain,
% 1.97/2.17 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8937])).
% 1.97/2.17 tff(8939,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[8938])).
% 1.97/2.17 tff(8940,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4249, 189, 8520, 118])).
% 1.97/2.17 tff(8941,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[524, 8940])).
% 1.97/2.17 tff(8942,plain,
% 1.97/2.17 (b(elem!1, s(s(s(z))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8941, 8939])).
% 1.97/2.17 tff(8943,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8936])).
% 1.97/2.17 tff(8944,plain,
% 1.97/2.17 (b(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8914, 8943])).
% 1.97/2.17 tff(8945,plain,
% 1.97/2.17 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8936])).
% 1.97/2.17 tff(8946,plain,
% 1.97/2.17 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(z))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8945, 119])).
% 1.97/2.17 tff(8947,plain,
% 1.97/2.17 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 1.97/2.17 inference(transitivity,[status(thm)],[8946, 120])).
% 1.97/2.17 tff(8948,plain,
% 1.97/2.17 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(z) = elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8947])).
% 1.97/2.17 tff(8949,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[516, 8948])).
% 1.97/2.17 tff(8950,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8936])).
% 1.97/2.17 tff(8951,plain,
% 1.97/2.17 (r(elem!1, s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8520, 8950])).
% 1.97/2.17 tff(8952,plain,
% 1.97/2.17 (~r(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3859, 8951, 8866])).
% 1.97/2.17 tff(8953,plain,
% 1.97/2.17 (b(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1759, 8952, 68])).
% 1.97/2.17 tff(8954,plain,
% 1.97/2.17 (~b(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2456, 8953, 8863, 8944])).
% 1.97/2.17 tff(8955,plain,
% 1.97/2.17 (r(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[921, 8954, 61])).
% 1.97/2.17 tff(8956,plain,
% 1.97/2.17 (~r(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3855, 8955, 8866])).
% 1.97/2.17 tff(8957,plain,
% 1.97/2.17 (b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[727, 8956, 8949])).
% 1.97/2.17 tff(8958,plain,
% 1.97/2.17 (~b(elem!1, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3935, 337, 8953, 8957, 1301, 8863, 8944])).
% 1.97/2.17 tff(8959,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8958, 8942])).
% 1.97/2.17 tff(8960,plain,(b(s(z), z) | (~b(z, s(z))) | b(s(s(s(s(z)))), s(z)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8961,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8960, 8935, 8519, 1925, 50, 1301, 118, 4370])).
% 1.97/2.17 tff(8962,plain,
% 1.97/2.17 (~b(s(s(s(elem!1))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8532, 8961, 1925, 1301])).
% 1.97/2.17 tff(8963,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.97/2.17 tff(8964,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.97/2.17 tff(8965,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[227, 43, 8964, 8963, 213])).
% 1.97/2.17 tff(8966,plain,(r(s(s(s(elem!1))), s(z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8967,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8966, 8962])).
% 1.97/2.17 tff(8968,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7192, 337, 1301, 8172, 8168])).
% 1.97/2.17 tff(8969,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1792, 8968])).
% 1.97/2.17 tff(8970,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8971,plain,
% 1.97/2.17 (((~b(s(s(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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(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))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8972,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8971])).
% 1.97/2.17 tff(8973,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8972, 8970])).
% 1.97/2.17 tff(8974,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8975,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8974, 8973])).
% 1.97/2.17 tff(8976,plain,
% 1.97/2.17 (~b(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8975, 337, 1301, 8172, 8168])).
% 1.97/2.17 tff(8977,plain,
% 1.97/2.17 (r(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1786, 8976])).
% 1.97/2.17 tff(8978,plain,
% 1.97/2.17 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8641, 8168, 4370])).
% 1.97/2.17 tff(8979,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3403, 8976, 1925])).
% 1.97/2.17 tff(8980,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[249, 8979])).
% 1.97/2.17 tff(8981,plain,
% 1.97/2.17 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5133, 8977, 1301, 1339])).
% 1.97/2.17 tff(8982,plain,
% 1.97/2.17 (b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2268, 8981])).
% 1.97/2.17 tff(8983,plain,
% 1.97/2.17 (((~b(s(z), s(s(s(s(z)))))) | (~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(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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8984,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8983])).
% 1.97/2.17 tff(8985,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8984, 3051])).
% 1.97/2.17 tff(8986,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8987,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[8986, 8985])).
% 1.97/2.18 tff(8988,plain,
% 1.97/2.18 (~b(s(s(z)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8987, 337, 8172, 8168, 8982])).
% 1.97/2.18 tff(8989,plain,
% 1.97/2.18 (r(s(s(z)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2229, 8988])).
% 1.97/2.18 tff(8990,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7348, 189, 118, 8989])).
% 1.97/2.18 tff(8991,plain,
% 1.97/2.18 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2854, 8990])).
% 1.97/2.18 tff(8992,plain,
% 1.97/2.18 (~r(s(s(z)), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1293, 189, 118, 8989])).
% 1.97/2.18 tff(8993,plain,
% 1.97/2.18 (b(s(s(z)), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4268, 8992])).
% 1.97/2.18 tff(8994,plain,
% 1.97/2.18 (~b(z, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7507, 8993, 1339, 8977, 8991])).
% 1.97/2.18 tff(8995,plain,
% 1.97/2.18 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1943, 8979])).
% 1.97/2.18 tff(8996,plain,
% 1.97/2.18 (r(elem!1, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[322, 8979, 4370])).
% 1.97/2.18 tff(8997,plain,
% 1.97/2.18 (~b(s(z), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1239, 337, 8172, 8168, 8982])).
% 1.97/2.18 tff(8998,plain,
% 1.97/2.18 (r(s(z), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8207, 8997])).
% 1.97/2.18 tff(8999,plain,
% 1.97/2.18 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.97/2.18 inference(commutativity,[status(thm)],[])).
% 1.97/2.18 tff(9000,plain,
% 1.97/2.18 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.97/2.18 inference(symmetry,[status(thm)],[8999])).
% 1.97/2.18 tff(9001,plain,
% 1.97/2.18 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9000])).
% 1.97/2.18 tff(9002,plain,
% 1.97/2.18 (~(z = s(s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[31, 9001])).
% 1.97/2.18 tff(9003,plain,
% 1.97/2.18 (((~![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))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9004,plain,
% 1.97/2.18 ((~![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))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9005,plain,
% 1.97/2.18 ((~![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)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9004, 9003])).
% 1.97/2.18 tff(9006,plain,
% 1.97/2.18 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9005, 43, 8994])).
% 1.97/2.18 tff(9007,plain,
% 1.97/2.18 (r(z, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9006, 9002])).
% 1.97/2.18 tff(9008,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9009,plain,
% 1.97/2.18 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9010,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9009])).
% 1.97/2.18 tff(9011,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9010, 9008])).
% 1.97/2.18 tff(9012,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9013,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9012, 9011])).
% 1.97/2.18 tff(9014,plain,
% 1.97/2.18 (~r(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9013, 189, 9007, 8998])).
% 1.97/2.18 tff(9015,plain,
% 1.97/2.18 (b(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[963, 9014])).
% 1.97/2.18 tff(9016,plain,
% 1.97/2.18 (~b(s(s(s(elem!1))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8532, 9015, 1925, 1301])).
% 1.97/2.18 tff(9017,plain,
% 1.97/2.18 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8966, 9016])).
% 1.97/2.18 tff(9018,plain,
% 1.97/2.18 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2153, 9017, 8996])).
% 1.97/2.18 tff(9019,plain,
% 1.97/2.18 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7411, 337, 1301, 8168, 8982, 8863, 8993])).
% 1.97/2.18 tff(9020,plain,
% 1.97/2.18 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[524, 9019])).
% 1.97/2.18 tff(9021,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9022,plain,
% 1.97/2.18 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9023,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(z, 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(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9022])).
% 1.97/2.18 tff(9024,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(z, 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(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9023, 9021])).
% 1.97/2.18 tff(9025,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9026,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9025, 9024])).
% 1.97/2.18 tff(9027,plain,
% 1.97/2.18 (~b(s(s(z)), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9026, 337, 1301, 8172, 8982, 8863, 8991])).
% 1.97/2.18 tff(9028,plain,
% 1.97/2.18 (r(s(s(z)), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2242, 9027])).
% 1.97/2.18 tff(9029,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9030,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9031,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9030, 9029])).
% 1.97/2.18 tff(9032,plain,
% 1.97/2.18 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9031, 189, 8969, 9028])).
% 1.97/2.18 tff(9033,plain,
% 1.97/2.18 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.97/2.18 inference(symmetry,[status(thm)],[7335])).
% 1.97/2.18 tff(9034,plain,
% 1.97/2.18 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9033])).
% 1.97/2.18 tff(9035,plain,
% 1.97/2.18 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[2263, 9034])).
% 1.97/2.18 tff(9036,plain,
% 1.97/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9037,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9038,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9037, 9036])).
% 1.97/2.18 tff(9039,plain,
% 1.97/2.18 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9038, 43])).
% 1.97/2.18 tff(9040,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9039, 9035])).
% 1.97/2.18 tff(9041,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9040, 9032])).
% 1.97/2.18 tff(9042,plain,
% 1.97/2.18 (~b(s(s(z)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8987, 337, 1275, 1231, 1396])).
% 1.97/2.18 tff(9043,plain,
% 1.97/2.18 (r(s(s(z)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2229, 9042])).
% 1.97/2.18 tff(9044,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9045,plain,
% 1.97/2.18 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9046,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9045])).
% 1.97/2.18 tff(9047,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9046, 9044])).
% 1.97/2.18 tff(9048,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9049,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9048, 9047])).
% 1.97/2.18 tff(9050,plain,
% 1.97/2.18 (~r(elem!1, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9049, 189, 777, 9043])).
% 1.97/2.18 tff(9051,plain,
% 1.97/2.18 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4164, 274, 1115])).
% 1.97/2.18 tff(9052,plain,
% 1.97/2.18 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2845, 43, 4102, 9051])).
% 1.97/2.18 tff(9053,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[857, 5327, 853])).
% 1.97/2.18 tff(9054,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9055,plain,
% 1.97/2.18 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9056,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9055])).
% 1.97/2.18 tff(9057,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9056, 9054])).
% 1.97/2.18 tff(9058,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9059,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9058, 9057])).
% 1.97/2.18 tff(9060,plain,
% 1.97/2.18 (~b(elem!1, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9059, 337, 9053, 1396, 9052])).
% 1.97/2.18 tff(9061,plain,
% 1.97/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9062,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9063,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9062, 9061])).
% 1.97/2.18 tff(9064,plain,
% 1.97/2.18 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9063, 43])).
% 1.97/2.18 tff(9065,plain,
% 1.97/2.18 (elem!1 = s(s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9064, 9060, 9050])).
% 1.97/2.18 tff(9066,plain,
% 1.97/2.18 (s(s(z)) = elem!1),
% 1.97/2.18 inference(symmetry,[status(thm)],[9065])).
% 1.97/2.18 tff(9067,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9066])).
% 1.97/2.18 tff(9068,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9067])).
% 1.97/2.18 tff(9069,plain,
% 1.97/2.18 (s(elem!1) = s(s(s(z)))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9065])).
% 1.97/2.18 tff(9070,plain,
% 1.97/2.18 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9069])).
% 1.97/2.18 tff(9071,plain,
% 1.97/2.18 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9070])).
% 1.97/2.18 tff(9072,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9071])).
% 1.97/2.18 tff(9073,plain,
% 1.97/2.18 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5731, 4102])).
% 1.97/2.18 tff(9074,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[857, 853, 803])).
% 1.97/2.18 tff(9075,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5347, 337, 791, 9074, 1231, 9073])).
% 1.97/2.18 tff(9076,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(9077,plain,
% 1.97/2.18 (~b(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9076, 9051, 1231, 853, 5327])).
% 1.97/2.18 tff(9078,plain,
% 1.97/2.18 (r(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[727, 9077, 2754])).
% 1.97/2.18 tff(9079,plain,
% 1.97/2.18 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9065])).
% 1.97/2.18 tff(9080,plain,
% 1.97/2.18 (b(z, s(s(z))) <=> b(z, elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9079])).
% 1.97/2.18 tff(9081,plain,
% 1.97/2.18 ((~b(z, s(s(z)))) <=> (~b(z, elem!1))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9080])).
% 1.97/2.18 tff(9082,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.97/2.18 tff(9083,plain,
% 1.97/2.18 (~b(z, elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9082, 9081])).
% 1.97/2.18 tff(9084,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8725, 9083, 1925, 9078, 61])).
% 1.97/2.18 tff(9085,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9084, 9072])).
% 1.97/2.18 tff(9086,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9085, 9068])).
% 1.97/2.18 tff(9087,plain,
% 1.97/2.18 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9071])).
% 1.97/2.18 tff(9088,plain,
% 1.97/2.18 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9087, 5506])).
% 1.97/2.18 tff(9089,plain,
% 1.97/2.18 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9088])).
% 1.97/2.18 tff(9090,plain,
% 1.97/2.18 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[4560, 9089])).
% 1.97/2.18 tff(9091,plain,
% 1.97/2.18 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9071, 9069])).
% 1.97/2.18 tff(9092,plain,
% 1.97/2.18 (~r(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5156, 189, 777, 9043])).
% 1.97/2.18 tff(9093,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(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(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9094,plain,
% 1.97/2.18 (((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9095,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(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(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9094])).
% 1.97/2.18 tff(9096,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(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(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9095, 9093])).
% 1.97/2.18 tff(9097,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(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)))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9098,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9097, 9096])).
% 1.97/2.18 tff(9099,plain,
% 1.97/2.18 (~b(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9098, 337, 1275, 1231, 1396, 9052])).
% 1.97/2.18 tff(9100,plain,
% 1.97/2.18 (s(s(z)) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2301, 9099, 9092])).
% 1.97/2.18 tff(9101,plain,
% 1.97/2.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[155, 9100, 50])).
% 1.97/2.18 tff(9102,plain,
% 1.97/2.18 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9069, 9065])).
% 1.97/2.18 tff(9103,plain,
% 1.97/2.18 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9102])).
% 1.97/2.18 tff(9104,plain,
% 1.97/2.18 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(elem!1), elem!1))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9103])).
% 1.97/2.18 tff(9105,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7348, 189, 118, 9043])).
% 1.97/2.18 tff(9106,plain,
% 1.97/2.18 (~r(s(elem!1), elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9105, 9104])).
% 1.97/2.18 tff(9107,plain,
% 1.97/2.18 (~(s(elem!1) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2773, 9100])).
% 1.97/2.19 tff(9108,plain,
% 1.97/2.19 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9069])).
% 1.97/2.19 tff(9109,plain,
% 1.97/2.19 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9108])).
% 1.97/2.19 tff(9110,plain,
% 1.97/2.19 (r(s(elem!1), s(z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[118, 9109])).
% 1.97/2.19 tff(9111,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7250, 9110, 2451, 777, 1899, 118, 9107, 9106])).
% 1.97/2.19 tff(9112,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[363, 9111, 9101])).
% 1.97/2.19 tff(9113,plain,
% 1.97/2.19 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9112, 9091])).
% 1.97/2.19 tff(9114,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9115,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9116,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9115, 9114])).
% 1.97/2.19 tff(9117,plain,
% 1.97/2.19 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9116, 189, 6489, 9113])).
% 1.97/2.19 tff(9118,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6726, 9117, 9090])).
% 1.97/2.19 tff(9119,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9120,plain,
% 1.97/2.19 (((~b(s(s(s(s(z)))), 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)))), 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9121,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, X4)) | (~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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9120])).
% 1.97/2.19 tff(9122,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, X4)) | (~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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9121, 9119])).
% 1.97/2.19 tff(9123,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9124,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9123, 9122])).
% 1.97/2.19 tff(9125,plain,
% 1.97/2.19 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9124, 337, 1231, 1396, 7465])).
% 1.97/2.19 tff(9126,plain,
% 1.97/2.19 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9125, 9118])).
% 1.97/2.19 tff(9127,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9126, 9086])).
% 1.97/2.19 tff(9128,plain,((~r(elem!1, z)) | (~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(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(z, s(s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(z)))))) | (s(z) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9129,plain,
% 1.97/2.19 (~r(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9128, 8168, 8982, 9041, 9020, 8996, 9018, 118, 1925, 8995, 8994, 50, 8172, 8980, 8978, 8977, 8969])).
% 1.97/2.19 tff(9130,plain,
% 1.97/2.19 (b(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1759, 9129, 68])).
% 1.97/2.19 tff(9131,plain,
% 1.97/2.19 (~r(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3923, 189, 8996, 118])).
% 1.97/2.19 tff(9132,plain,
% 1.97/2.19 (~b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5083, 337, 9130, 9015, 1301, 8863])).
% 1.97/2.19 tff(9133,plain,
% 1.97/2.19 (s(s(s(z))) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2463, 9132, 9131])).
% 1.97/2.19 tff(9134,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7671, 9133, 2451])).
% 1.97/2.19 tff(9135,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[350, 9134, 9018])).
% 1.97/2.19 tff(9136,plain,
% 1.97/2.19 (~b(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7655, 9135, 9130, 1925])).
% 1.97/2.19 tff(9137,plain,
% 1.97/2.19 (~b(s(z), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4379, 337, 9130, 9015, 1301])).
% 1.97/2.19 tff(9138,plain,
% 1.97/2.19 (r(s(z), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[727, 9137, 8980])).
% 1.97/2.19 tff(9139,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1472, 9133])).
% 1.97/2.19 tff(9140,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2743, 9139, 8979])).
% 1.97/2.19 tff(9141,plain,
% 1.97/2.19 (r(s(elem!1), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8701, 9135, 50, 1925, 1301, 9015, 9130, 9140, 8996])).
% 1.97/2.19 tff(9142,plain,
% 1.97/2.19 (~r(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6190, 9141, 50, 1301, 9138])).
% 1.97/2.19 tff(9143,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[921, 9142, 9136, 61])).
% 1.97/2.19 tff(9144,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9145,plain,
% 1.97/2.19 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9144, 4370, 1301, 1925, 118, 50])).
% 1.97/2.19 tff(9146,plain,
% 1.97/2.19 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[548, 9145])).
% 1.97/2.19 tff(9147,plain,
% 1.97/2.19 (~b(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4327, 337, 8941, 9146, 8933])).
% 1.97/2.19 tff(9148,plain,
% 1.97/2.19 (~r(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3916, 189, 8930, 118])).
% 1.97/2.19 tff(9149,plain,
% 1.97/2.19 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5966, 43, 9148])).
% 1.97/2.19 tff(9150,plain,
% 1.97/2.19 (elem!1 = s(s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9149, 9147])).
% 1.97/2.19 tff(9151,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.19 inference(symmetry,[status(thm)],[8610])).
% 1.97/2.19 tff(9152,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9151])).
% 1.97/2.19 tff(9153,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9152])).
% 1.97/2.19 tff(9154,plain,
% 1.97/2.19 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[8610])).
% 1.97/2.19 tff(9155,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9154])).
% 1.97/2.19 tff(9156,plain,
% 1.97/2.19 (r(s(elem!1), s(z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[811, 9155])).
% 1.97/2.19 tff(9157,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2153, 214, 777])).
% 1.97/2.19 tff(9158,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7250, 9157, 2470, 777, 3062, 118, 265, 9156])).
% 1.97/2.19 tff(9159,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[363, 9158, 172])).
% 1.97/2.19 tff(9160,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9159, 9153])).
% 1.97/2.19 tff(9161,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9162,plain,
% 1.97/2.19 (((~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(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9163,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9162])).
% 1.97/2.19 tff(9164,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9163, 9161])).
% 1.97/2.19 tff(9165,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9166,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9165, 9164])).
% 1.97/2.19 tff(9167,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9166, 189, 811, 214])).
% 1.97/2.19 tff(9168,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9167, 9160])).
% 1.97/2.19 tff(9169,plain,((~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | r(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9170,plain,
% 1.97/2.19 (r(s(elem!1), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9169, 9150, 8520, 8934, 2451, 8930, 8967, 118])).
% 1.97/2.19 tff(9171,plain,
% 1.97/2.19 (~r(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3923, 189, 8930, 118])).
% 1.97/2.19 tff(9172,plain,
% 1.97/2.19 (~b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4952, 337, 8941, 9146, 8933])).
% 1.97/2.19 tff(9173,plain,
% 1.97/2.19 (s(s(s(z))) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2463, 9172, 9171])).
% 1.97/2.19 tff(9174,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1472, 9173])).
% 1.97/2.19 tff(9175,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[809, 9174, 9170, 8931])).
% 1.97/2.19 tff(9176,plain,(b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9177,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9176, 853, 1925, 1301, 50, 4370, 118])).
% 1.97/2.19 tff(9178,plain,
% 1.97/2.19 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5931])).
% 1.97/2.19 tff(9179,plain,
% 1.97/2.19 (~r(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3859, 777, 275])).
% 1.97/2.19 tff(9180,plain,
% 1.97/2.19 (b(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1759, 9179, 3768])).
% 1.97/2.19 tff(9181,plain,
% 1.97/2.19 (~r(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3855, 1735, 275])).
% 1.97/2.19 tff(9182,plain,
% 1.97/2.19 (b(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[921, 9181, 65])).
% 1.97/2.19 tff(9183,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7655, 9182, 9180, 1925])).
% 1.97/2.19 tff(9184,plain,
% 1.97/2.19 (~b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2456, 9182, 1659, 9180])).
% 1.97/2.19 tff(9185,plain,
% 1.97/2.19 (s(s(s(z))) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2463, 9184, 2461])).
% 1.97/2.19 tff(9186,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7671, 9185, 2470])).
% 1.97/2.19 tff(9187,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[350, 9186, 9183])).
% 1.97/2.19 tff(9188,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2153, 9187, 777])).
% 1.97/2.19 tff(9189,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8966, 9188])).
% 1.97/2.19 tff(9190,plain,
% 1.97/2.19 (~r(s(z), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2164, 189, 9187, 1735])).
% 1.97/2.19 tff(9191,plain,
% 1.97/2.19 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1970, 9190])).
% 1.97/2.19 tff(9192,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9193,plain,
% 1.97/2.19 (((~b(s(s(s(elem!1))), s(z))) | (~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(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9194,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(z))) | (~b(s(z), s(s(s(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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9193])).
% 1.97/2.19 tff(9195,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(z))) | (~b(s(z), s(s(s(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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9194, 9192])).
% 1.97/2.19 tff(9196,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9197,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9196, 9195])).
% 1.97/2.19 tff(9198,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9197, 337, 1925, 1301, 9191, 9189])).
% 1.97/2.19 tff(9199,plain,((~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9200,plain,
% 1.97/2.19 (~r(s(z), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9199, 4406, 1301, 1925, 2451, 8653, 8863, 61, 275])).
% 1.97/2.19 tff(9201,plain,
% 1.97/2.19 (b(s(z), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[727, 9200, 272])).
% 1.97/2.19 tff(9202,plain,
% 1.97/2.19 (~b(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4005, 9201, 1301, 8868])).
% 1.97/2.19 tff(9203,plain,
% 1.97/2.19 (~(s(elem!1) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7830, 9202, 1925])).
% 1.97/2.19 tff(9204,plain,
% 1.97/2.19 (r(z, elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[921, 9202, 61])).
% 1.97/2.19 tff(9205,plain,
% 1.97/2.19 (~r(s(elem!1), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6204, 9204, 1301, 50, 8868, 247])).
% 1.97/2.19 tff(9206,plain,
% 1.97/2.19 (b(s(elem!1), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[270, 9205, 9203])).
% 1.97/2.19 tff(9207,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[1470])).
% 1.97/2.19 tff(9208,plain,
% 1.97/2.19 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[1469])).
% 1.97/2.19 tff(9209,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[2, 9208])).
% 1.97/2.19 tff(9210,plain,
% 1.97/2.19 (b(elem!1, s(elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9209, 9207])).
% 1.97/2.19 tff(9211,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[1470])).
% 1.97/2.19 tff(9212,plain,
% 1.97/2.19 (b(s(elem!1), s(z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[1231, 9211])).
% 1.97/2.19 tff(9213,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9214,plain,
% 1.97/2.19 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9215,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9214])).
% 1.97/2.19 tff(9216,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9215, 9213])).
% 1.97/2.19 tff(9217,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9218,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9217, 9216])).
% 1.97/2.19 tff(9219,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9218, 337, 2520, 9212, 791, 9210])).
% 1.97/2.19 tff(9220,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9221,plain,
% 1.97/2.19 (~(s(s(s(z))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9220, 9206, 9201, 1231, 9146])).
% 1.97/2.19 tff(9222,plain,
% 1.97/2.19 (~(elem!1 = s(s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9221, 9178])).
% 1.97/2.19 tff(9223,plain,
% 1.97/2.19 (b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2463, 9221, 8653])).
% 1.97/2.19 tff(9224,plain,
% 1.97/2.19 (~b(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3935, 337, 8868, 9201, 1301, 8863, 9223])).
% 1.97/2.19 tff(9225,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8619, 9224, 9222])).
% 1.97/2.19 tff(9226,plain,((elem!1 = s(z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9227,plain,
% 1.97/2.19 (elem!1 = s(z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9226, 8866, 1231, 50, 1925, 1301, 118, 4370])).
% 1.97/2.19 tff(9228,plain,
% 1.97/2.19 (b(z, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3403, 9227, 1925])).
% 1.97/2.19 tff(9229,plain,
% 1.97/2.19 (~b(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6686, 9227, 6683])).
% 1.97/2.19 tff(9230,plain,
% 1.97/2.19 (r(elem!1, z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1759, 9229, 68])).
% 1.97/2.19 tff(9231,plain,
% 1.97/2.19 (s(elem!1) = s(s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9227])).
% 1.97/2.19 tff(9232,plain,
% 1.97/2.19 (s(s(elem!1)) = s(s(s(z)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9231])).
% 1.97/2.19 tff(9233,plain,
% 1.97/2.19 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9232])).
% 1.97/2.19 tff(9234,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9233])).
% 1.97/2.19 tff(9235,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(symmetry,[status(thm)],[9234])).
% 1.97/2.19 tff(9236,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1795, 9228, 8863, 9146])).
% 1.97/2.19 tff(9237,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1792, 9236])).
% 1.97/2.19 tff(9238,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9237, 9235])).
% 1.97/2.19 tff(9239,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9240,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9241,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9240, 9239])).
% 1.97/2.19 tff(9242,plain,
% 1.97/2.19 ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9241, 189])).
% 1.97/2.19 tff(9243,plain,
% 1.97/2.19 (~r(elem!1, s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9242, 9238, 9230])).
% 1.97/2.19 tff(9244,plain,
% 1.97/2.19 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1144, 9243, 9227])).
% 1.97/2.19 tff(9245,plain,
% 1.97/2.19 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1150, 9244])).
% 1.97/2.19 tff(9246,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8975, 337, 1301, 9245, 1231, 9228])).
% 1.97/2.19 tff(9247,plain,(b(s(z), z) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9248,plain,
% 1.97/2.19 (b(s(z), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9247, 9177, 1301, 1925, 50, 118, 4370])).
% 1.97/2.19 tff(9249,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8561, 337, 1925, 9248, 1301, 9177])).
% 1.97/2.19 tff(9250,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1792, 9249])).
% 1.97/2.19 tff(9251,plain,
% 1.97/2.19 (~b(z, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4738, 337, 9248, 1301, 9177])).
% 1.97/2.19 tff(9252,plain,
% 1.97/2.19 (r(z, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1786, 9251])).
% 1.97/2.19 tff(9253,plain,
% 1.97/2.19 (~(elem!1 = s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3403, 9251, 1925])).
% 1.97/2.19 tff(9254,plain,
% 1.97/2.19 (r(elem!1, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[322, 9253, 4370])).
% 1.97/2.19 tff(9255,plain,
% 1.97/2.19 (~r(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3916, 189, 9254, 118])).
% 1.97/2.19 tff(9256,plain,
% 1.97/2.19 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4164, 6588, 1115])).
% 1.97/2.19 tff(9257,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2845, 43, 4102, 9256])).
% 1.97/2.19 tff(9258,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1177, 6588, 1168])).
% 1.97/2.19 tff(9259,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[857, 9258, 853])).
% 1.97/2.19 tff(9260,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9261,plain,
% 1.97/2.19 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9262,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9261])).
% 2.04/2.20 tff(9263,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9262, 9260])).
% 2.04/2.20 tff(9264,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9265,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9264, 9263])).
% 2.04/2.20 tff(9266,plain,
% 2.04/2.20 (~b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9265, 337, 2, 9259, 9257])).
% 2.04/2.20 tff(9267,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.04/2.20 tff(9268,plain,
% 2.04/2.20 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5966, 43, 9267])).
% 2.04/2.20 tff(9269,plain,
% 2.04/2.20 (elem!1 = s(s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9268, 9266])).
% 2.04/2.20 tff(9270,plain,
% 2.04/2.20 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9269])).
% 2.04/2.20 tff(9271,plain,
% 2.04/2.20 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 2.04/2.20 inference(symmetry,[status(thm)],[9270])).
% 2.04/2.20 tff(9272,plain,
% 2.04/2.20 (b(elem!1, z)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[1659, 9271])).
% 2.04/2.20 tff(9273,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4858, 9272])).
% 2.04/2.20 tff(9274,plain,(b(elem!1, z) | (~b(s(s(s(z))), z)) | r(elem!1, s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9275,plain,
% 2.04/2.20 (b(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9274, 9255, 8863, 9146, 853, 9252, 9250, 68])).
% 2.04/2.20 tff(9276,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8532, 9248, 1925, 1301])).
% 2.04/2.20 tff(9277,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8966, 9276])).
% 2.04/2.20 tff(9278,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2153, 9254, 9277])).
% 2.04/2.20 tff(9279,plain,
% 2.04/2.20 (~r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3923, 189, 9254, 118])).
% 2.04/2.20 tff(9280,plain,
% 2.04/2.20 (~b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5083, 337, 9275, 9248, 1301, 8863])).
% 2.04/2.20 tff(9281,plain,
% 2.04/2.20 (s(s(s(z))) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2463, 9280, 9279])).
% 2.04/2.20 tff(9282,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7671, 9281, 2451])).
% 2.04/2.20 tff(9283,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[350, 9282, 9278])).
% 2.04/2.20 tff(9284,plain,
% 2.04/2.20 (~b(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7655, 9283, 9275, 1925])).
% 2.04/2.20 tff(9285,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9286,plain,
% 2.04/2.20 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9287,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9286])).
% 2.04/2.20 tff(9288,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9287, 9285])).
% 2.04/2.20 tff(9289,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9290,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9289, 9288])).
% 2.04/2.20 tff(9291,plain,
% 2.04/2.20 (~b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9290, 337, 9275, 9248, 1301, 8863])).
% 2.04/2.20 tff(9292,plain,
% 2.04/2.20 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5966, 43, 9255])).
% 2.04/2.20 tff(9293,plain,
% 2.04/2.20 (elem!1 = s(s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9292, 9291])).
% 2.04/2.20 tff(9294,plain,
% 2.04/2.20 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8610])).
% 2.04/2.20 tff(9295,plain,
% 2.04/2.20 (b(z, s(s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[600, 9294])).
% 2.04/2.20 tff(9296,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1784, 9295])).
% 2.04/2.20 tff(9297,plain,((~b(z, s(elem!1))) | b(z, s(s(s(s(z))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9298,plain,
% 2.04/2.20 (~b(z, s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9297, 9293, 9251])).
% 2.04/2.20 tff(9299,plain,
% 2.04/2.20 (r(z, s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[395, 9298])).
% 2.04/2.20 tff(9300,plain,
% 2.04/2.20 (s(s(s(s(z)))) = s(elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1472, 9281])).
% 2.04/2.20 tff(9301,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2743, 9300, 9253])).
% 2.04/2.20 tff(9302,plain,
% 2.04/2.20 (r(s(elem!1), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8701, 9283, 50, 1925, 1301, 9248, 9275, 9301, 9254])).
% 2.04/2.20 tff(9303,plain,
% 2.04/2.20 (~r(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1748, 9302, 9299])).
% 2.04/2.20 tff(9304,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[921, 9303, 9284, 61])).
% 2.04/2.20 tff(9305,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9306,plain,
% 2.04/2.20 (s(s(s(s(z)))) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9305, 4370, 50, 1301, 118, 1925])).
% 2.04/2.20 tff(9307,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8641, 9306, 4370])).
% 2.04/2.20 tff(9308,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[170, 9306, 50])).
% 2.04/2.20 tff(9309,plain,
% 2.04/2.20 (~(s(elem!1) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[264, 9308])).
% 2.04/2.20 tff(9310,plain,
% 2.04/2.20 (b(s(z), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8960, 9309, 9307, 1925, 50, 1301, 118, 4370])).
% 2.04/2.20 tff(9311,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[851, 9307])).
% 2.04/2.20 tff(9312,plain,
% 2.04/2.20 (~b(z, s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4313, 9311, 1301, 8863, 9310])).
% 2.04/2.20 tff(9313,plain,
% 2.04/2.20 (~(elem!1 = s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3403, 9312, 1925])).
% 2.04/2.20 tff(9314,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1943, 9313])).
% 2.04/2.20 tff(9315,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8532, 9310, 1925, 1301])).
% 2.04/2.20 tff(9316,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8966, 9315])).
% 2.04/2.20 tff(9317,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8553, 9316, 9311, 118, 9314])).
% 2.04/2.20 tff(9318,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6407, 43, 9317, 8518])).
% 2.04/2.20 tff(9319,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9306])).
% 2.04/2.20 tff(9320,plain,
% 2.04/2.20 (b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9146, 9319])).
% 2.04/2.20 tff(9321,plain,
% 2.04/2.20 (r(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[322, 9313, 4370])).
% 2.04/2.20 tff(9322,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2153, 9321, 9316])).
% 2.04/2.20 tff(9323,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[801, 9313, 9306])).
% 2.04/2.20 tff(9324,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[350, 9323, 9322])).
% 2.04/2.20 tff(9325,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9326,plain,
% 2.04/2.20 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9327,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9326])).
% 2.04/2.20 tff(9328,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9327, 9325])).
% 2.04/2.20 tff(9329,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9330,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9329, 9328])).
% 2.04/2.20 tff(9331,plain,
% 2.04/2.20 (~b(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9330, 337, 9324, 1925, 9310, 8863, 9320])).
% 2.04/2.20 tff(9332,plain,
% 2.04/2.20 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2796, 43, 9331])).
% 2.04/2.20 tff(9333,plain,
% 2.04/2.20 (r(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9332, 2781])).
% 2.04/2.20 tff(9334,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9335,plain,
% 2.04/2.20 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9336,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9335])).
% 2.04/2.20 tff(9337,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9336, 9334])).
% 2.04/2.20 tff(9338,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9339,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9338, 9337])).
% 2.04/2.20 tff(9340,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9339, 189, 9316, 9333, 9318])).
% 2.04/2.20 tff(9341,plain,(b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9342,plain,
% 2.04/2.20 (b(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9341, 7636, 49, 8513, 50])).
% 2.04/2.20 tff(9343,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5572, 9342, 3])).
% 2.04/2.20 tff(9344,plain,
% 2.04/2.20 (b(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9341, 1925, 118, 1301, 50])).
% 2.04/2.20 tff(9345,plain,
% 2.04/2.20 (~b(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[970, 337, 9344, 8524, 1301])).
% 2.04/2.20 tff(9346,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7903, 9345, 1925])).
% 2.04/2.20 tff(9347,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[281, 9346])).
% 2.04/2.20 tff(9348,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9349,plain,
% 2.04/2.20 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9350,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9349])).
% 2.04/2.20 tff(9351,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9350, 9348])).
% 2.04/2.20 tff(9352,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9353,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9352, 9351])).
% 2.04/2.20 tff(9354,plain,
% 2.04/2.20 (~b(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9353, 337, 9344, 1925, 8524, 1301])).
% 2.04/2.20 tff(9355,plain,
% 2.04/2.20 (r(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1759, 9354, 68])).
% 2.04/2.20 tff(9356,plain,
% 2.04/2.20 (r(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[921, 9345, 61])).
% 2.04/2.20 tff(9357,plain,
% 2.04/2.20 (~(elem!1 = s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6585, 9345, 1301])).
% 2.04/2.20 tff(9358,plain,
% 2.04/2.20 (~(s(z) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[249, 9357])).
% 2.04/2.20 tff(9359,plain,
% 2.04/2.20 (~b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7168, 1474, 327, 274, 1735, 1, 1301, 118, 853, 370])).
% 2.04/2.20 tff(9360,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2463, 9359, 5785, 1481])).
% 2.04/2.20 tff(9361,plain,((~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9362,plain,
% 2.04/2.20 (~r(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9361, 9355, 9344, 1474, 4645, 8524, 1301, 118, 853, 9356])).
% 2.04/2.20 tff(9363,plain,
% 2.04/2.20 (b(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[727, 9362, 9358])).
% 2.04/2.20 tff(9364,plain,
% 2.04/2.20 (~r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4211, 9356, 1474])).
% 2.04/2.20 tff(9365,plain,
% 2.04/2.20 (b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2463, 9364, 4645])).
% 2.04/2.20 tff(9366,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4287, 9363, 9344, 8545, 9365])).
% 2.04/2.20 tff(9367,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[857, 9366, 853])).
% 2.04/2.20 tff(9368,plain,
% 2.04/2.20 (s(s(z)) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4277, 9367, 1301, 9344, 4102, 118, 9363, 8524, 9356, 4645, 9355])).
% 2.04/2.20 tff(9369,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[155, 9368, 50])).
% 2.04/2.20 tff(9370,plain,
% 2.04/2.20 (~(s(elem!1) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7830, 9345, 1925])).
% 2.04/2.20 tff(9371,plain,
% 2.04/2.20 (s(s(s(z))) = s(elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9368])).
% 2.04/2.20 tff(9372,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9371])).
% 2.04/2.20 tff(9373,plain,
% 2.04/2.20 (r(s(elem!1), s(z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[118, 9372])).
% 2.04/2.20 tff(9374,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9371])).
% 2.04/2.20 tff(9375,plain,
% 2.04/2.20 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9374])).
% 2.04/2.20 tff(9376,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4945, 9375])).
% 2.04/2.20 tff(9377,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1943, 9357])).
% 2.04/2.20 tff(9378,plain,
% 2.04/2.20 (s(elem!1) = s(s(s(z)))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9371])).
% 2.04/2.20 tff(9379,plain,
% 2.04/2.20 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9378])).
% 2.04/2.20 tff(9380,plain,
% 2.04/2.20 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.20 inference(symmetry,[status(thm)],[9379])).
% 2.04/2.20 tff(9381,plain,
% 2.04/2.20 (b(s(elem!1), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9365, 9380])).
% 2.04/2.20 tff(9382,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9383,plain,
% 2.04/2.20 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9384,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9383])).
% 2.04/2.21 tff(9385,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9384, 9382])).
% 2.04/2.21 tff(9386,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9387,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9386, 9385])).
% 2.04/2.21 tff(9388,plain,
% 2.04/2.21 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9387, 337, 1, 1301, 3639])).
% 2.04/2.21 tff(9389,plain,
% 2.04/2.21 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1970, 9388])).
% 2.04/2.21 tff(9390,plain,
% 2.04/2.21 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5433, 9389, 788])).
% 2.04/2.21 tff(9391,plain,
% 2.04/2.21 (b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[579, 9390, 428])).
% 2.04/2.21 tff(9392,assumption,(~r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 2.04/2.21 tff(9393,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9394,plain,
% 2.04/2.21 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), 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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9395,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9394])).
% 2.04/2.21 tff(9396,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9395, 9393])).
% 2.04/2.21 tff(9397,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9398,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9397, 9396])).
% 2.04/2.21 tff(9399,plain,
% 2.04/2.21 (~b(s(s(s(elem!1))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9398, 337, 1925, 1, 3639])).
% 2.04/2.21 tff(9400,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[227, 43, 9399, 213])).
% 2.04/2.21 tff(9401,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9402,plain,
% 2.04/2.21 (((~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(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9403,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9402])).
% 2.04/2.21 tff(9404,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9403, 9401])).
% 2.04/2.21 tff(9405,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9406,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9405, 9404])).
% 2.04/2.21 tff(9407,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9406, 189, 788, 9400])).
% 2.04/2.21 tff(9408,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[363, 9407, 172])).
% 2.04/2.21 tff(9409,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9410,plain,
% 2.04/2.21 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(s(z)))), z))) <=> ((~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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9411,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9410])).
% 2.04/2.21 tff(9412,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9411, 9409])).
% 2.04/2.21 tff(9413,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(s(z)))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9414,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9413, 9412])).
% 2.04/2.21 tff(9415,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9414, 337, 365, 638, 1925, 7071])).
% 2.04/2.21 tff(9416,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1792, 9415])).
% 2.04/2.21 tff(9417,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1177, 9416, 274])).
% 2.04/2.21 tff(9418,plain,
% 2.04/2.21 (s(s(s(s(z)))) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[857, 9417, 229])).
% 2.04/2.21 tff(9419,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), 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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9420,plain,
% 2.04/2.21 (((~b(s(elem!1), elem!1)) | (~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(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9421,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z)))), s(s(s(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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9420])).
% 2.04/2.21 tff(9422,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z)))), s(s(s(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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9421, 9419])).
% 2.04/2.21 tff(9423,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9424,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9423, 9422])).
% 2.04/2.21 tff(9425,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9424, 337, 365, 2520, 638, 7071])).
% 2.04/2.21 tff(9426,plain,
% 2.04/2.21 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[832, 43, 9392])).
% 2.04/2.21 tff(9427,plain,
% 2.04/2.21 (s(s(s(s(z)))) = s(elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9426, 9425])).
% 2.04/2.21 tff(9428,plain,
% 2.04/2.21 (s(elem!1) = s(s(s(s(z))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[9427])).
% 2.04/2.21 tff(9429,plain,
% 2.04/2.21 (s(elem!1) = elem!1),
% 2.04/2.21 inference(transitivity,[status(thm)],[9428, 9418])).
% 2.04/2.21 tff(9430,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[978, 9429])).
% 2.04/2.21 tff(9431,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (s(elem!1) = elem!1) | b(s(s(s(s(z)))), elem!1) | (~r(elem!1, z)) | r(s(s(s(s(z)))), s(elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9432,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9431, 9408, 229, 274, 9392, 978, 9391, 1925, 2520])).
% 2.04/2.21 tff(9433,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1947, 43, 4560, 9432])).
% 2.04/2.21 tff(9434,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9435,plain,
% 2.04/2.21 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9436,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9435])).
% 2.04/2.21 tff(9437,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9436, 9434])).
% 2.04/2.21 tff(9438,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~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)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9439,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9438, 9437])).
% 2.04/2.21 tff(9440,plain,
% 2.04/2.21 (~b(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9439, 337, 327, 2520, 9391, 1301, 3639])).
% 2.04/2.21 tff(9441,plain,
% 2.04/2.21 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[295, 43, 630, 9440])).
% 2.04/2.21 tff(9442,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2437, 189, 9441, 9433])).
% 2.04/2.21 tff(9443,plain,
% 2.04/2.21 (s(s(s(s(z)))) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[857, 9442, 229])).
% 2.04/2.21 tff(9444,plain,
% 2.04/2.21 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9443])).
% 2.04/2.21 tff(9445,plain,
% 2.04/2.21 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[9444])).
% 2.04/2.21 tff(9446,plain,
% 2.04/2.21 (b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[2520, 9445])).
% 2.04/2.21 tff(9447,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9448,plain,
% 2.04/2.21 (((~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))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9449,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9448])).
% 2.04/2.22 tff(9450,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9449, 9447])).
% 2.04/2.22 tff(9451,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9452,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9451, 9450])).
% 2.04/2.22 tff(9453,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9452, 189, 9389, 9433])).
% 2.04/2.22 tff(9454,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[851, 9453])).
% 2.04/2.22 tff(9455,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9456,plain,
% 2.04/2.22 (((~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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9457,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9456])).
% 2.04/2.22 tff(9458,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9457, 9455])).
% 2.04/2.22 tff(9459,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9460,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9459, 9458])).
% 2.04/2.22 tff(9461,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9460, 189, 9389, 9433])).
% 2.04/2.22 tff(9462,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1150, 9461])).
% 2.04/2.22 tff(9463,plain,
% 2.04/2.22 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2510, 9443, 50])).
% 2.04/2.22 tff(9464,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8251, 9443, 2461])).
% 2.04/2.22 tff(9465,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[548, 9464])).
% 2.04/2.22 tff(9466,plain,
% 2.04/2.22 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4847, 9465, 788, 1, 9463, 9462, 9454])).
% 2.04/2.22 tff(9467,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9466, 9446])).
% 2.04/2.22 tff(9468,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | r(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, z)) | r(s(s(s(s(z)))), s(elem!1)) | (s(elem!1) = elem!1) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9469,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9468, 9381, 8524, 9355, 9364, 50, 9366, 9377, 9376, 9373, 9370, 1925, 9369, 9347, 9344, 1301])).
% 2.04/2.22 tff(9470,plain,
% 2.04/2.22 (~b(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5630, 9381, 9344, 811, 9355, 9366, 9373, 1301, 829, 118, 50])).
% 2.04/2.22 tff(9471,plain,
% 2.04/2.22 (r(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[395, 9470])).
% 2.04/2.22 tff(9472,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9371])).
% 2.04/2.22 tff(9473,plain,
% 2.04/2.22 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9472])).
% 2.04/2.22 tff(9474,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8966, 8533])).
% 2.04/2.22 tff(9475,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8553, 9377, 811, 118, 9474])).
% 2.04/2.22 tff(9476,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9475, 9473])).
% 2.04/2.22 tff(9477,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[363, 9476, 9369])).
% 2.04/2.22 tff(9478,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3167, 9477, 9471])).
% 2.04/2.22 tff(9479,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[406, 43, 133, 9478, 9469])).
% 2.04/2.22 tff(9480,plain,((~r(s(s(s(z))), z)) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9481,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9480, 853, 1925, 1301, 811, 829, 118, 50])).
% 2.04/2.22 tff(9482,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1498, 9481])).
% 2.04/2.22 tff(9483,plain,
% 2.04/2.22 (~r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2896, 275, 274])).
% 2.04/2.22 tff(9484,plain,
% 2.04/2.22 (b(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[727, 9483, 272])).
% 2.04/2.22 tff(9485,plain,
% 2.04/2.22 (~r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3898, 9484, 1301, 118, 853, 275, 274, 1481, 247])).
% 2.04/2.22 tff(9486,plain,
% 2.04/2.22 (b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[921, 9485, 65])).
% 2.04/2.22 tff(9487,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4055, 337, 9486, 327, 9484, 1301])).
% 2.04/2.22 tff(9488,plain,((~r(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (z = elem!1) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9489,plain,
% 2.04/2.22 (~r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9488, 274, 1301, 61, 118, 853, 9344, 4645, 247])).
% 2.04/2.22 tff(9490,plain,
% 2.04/2.22 (b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[963, 9489])).
% 2.04/2.22 tff(9491,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[970, 337, 9344, 9490, 1301])).
% 2.04/2.22 tff(9492,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[921, 9491, 61])).
% 2.04/2.22 tff(9493,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7830, 9491, 1925])).
% 2.04/2.22 tff(9494,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3876, 9492, 118, 1301, 1659, 274])).
% 2.04/2.22 tff(9495,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[857, 9494, 853])).
% 2.04/2.22 tff(9496,plain,
% 2.04/2.22 (b(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2463, 4124, 1481])).
% 2.04/2.22 tff(9497,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4143, 9496, 327, 1603, 1735, 2842, 118])).
% 2.04/2.22 tff(9498,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1150, 9497])).
% 2.04/2.22 tff(9499,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9500,plain,
% 2.04/2.22 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, 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(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9501,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9500])).
% 2.04/2.22 tff(9502,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9501, 9499])).
% 2.04/2.22 tff(9503,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9504,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9503, 9502])).
% 2.04/2.22 tff(9505,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9504, 337, 327, 3243, 9498, 2, 1603, 9496])).
% 2.04/2.22 tff(9506,plain,((~r(s(z), elem!1)) | (~b(elem!1, 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(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9507,plain,
% 2.04/2.22 (~r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9506, 9495, 3243, 2, 9344, 4102, 118, 4645])).
% 2.04/2.22 tff(9508,plain,
% 2.04/2.22 (b(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[727, 9507, 272])).
% 2.04/2.22 tff(9509,plain,
% 2.04/2.22 (~b(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7156, 9508, 9344, 829, 9495, 50, 9490])).
% 2.04/2.22 tff(9510,plain,
% 2.04/2.22 (r(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[270, 9509, 9493])).
% 2.04/2.22 tff(9511,plain,
% 2.04/2.22 (~r(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1748, 9510, 9492])).
% 2.04/2.22 tff(9512,plain,
% 2.04/2.22 (b(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[395, 9511])).
% 2.04/2.22 tff(9513,plain,
% 2.04/2.22 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7903, 9491, 1925])).
% 2.04/2.22 tff(9514,plain,
% 2.04/2.22 (~r(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[374, 9510, 9492])).
% 2.04/2.22 tff(9515,plain,
% 2.04/2.22 (b(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[378, 43, 114, 9514])).
% 2.04/2.22 tff(9516,plain,
% 2.04/2.22 (~b(s(elem!1), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8824, 9515, 1301, 9490])).
% 2.04/2.22 tff(9517,plain,
% 2.04/2.22 (r(s(elem!1), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[898, 9516, 50])).
% 2.04/2.22 tff(9518,plain,
% 2.04/2.22 (~r(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8043, 788, 1925, 600, 273, 172, 327, 791, 276])).
% 2.04/2.22 tff(9519,plain,
% 2.04/2.22 (b(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[80, 9518])).
% 2.04/2.22 tff(9520,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4055, 337, 327, 791, 9519])).
% 2.04/2.22 tff(9521,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[921, 9520, 65])).
% 2.04/2.22 tff(9522,plain,
% 2.04/2.22 (~r(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[374, 9521, 273])).
% 2.04/2.22 tff(9523,plain,
% 2.04/2.22 (b(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[378, 43, 114, 9522])).
% 2.04/2.22 tff(9524,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[765, 9521, 273, 172])).
% 2.04/2.22 tff(9525,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[350, 9524, 276])).
% 2.04/2.22 tff(9526,plain,
% 2.04/2.22 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1977, 337, 327, 9525, 791])).
% 2.04/2.22 tff(9527,plain,
% 2.04/2.22 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[310, 43, 211, 9526])).
% 2.04/2.22 tff(9528,plain,
% 2.04/2.22 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5433, 9527, 788])).
% 2.04/2.22 tff(9529,plain,
% 2.04/2.22 (b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[579, 9528, 428])).
% 2.04/2.22 tff(9530,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9531,plain,
% 2.04/2.22 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~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))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9532,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9531])).
% 2.04/2.22 tff(9533,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9532, 9530])).
% 2.04/2.22 tff(9534,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9535,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9534, 9533])).
% 2.04/2.22 tff(9536,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9535, 337, 327, 9525, 9529, 1925, 9519, 9523])).
% 2.04/2.22 tff(9537,plain,((~r(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9538,plain,
% 2.04/2.22 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9537, 9517, 1925, 9344, 9508, 9513, 9510, 61, 9512])).
% 2.04/2.22 tff(9539,plain,
% 2.04/2.22 (~(s(s(z)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[155, 9538, 50])).
% 2.04/2.22 tff(9540,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4368, 9539, 9538, 1301, 9344, 9490, 118, 853, 61])).
% 2.04/2.22 tff(9541,plain,((~r(elem!1, z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9542,plain,
% 2.04/2.22 (~r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9541, 247, 118, 853, 50, 1925, 829, 3243, 2, 1659, 1301])).
% 2.04/2.22 tff(9543,plain,
% 2.04/2.22 (b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1759, 9542, 68])).
% 2.04/2.22 tff(9544,plain,
% 2.04/2.22 (~b(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3908, 9543, 1301, 9344])).
% 2.04/2.22 tff(9545,plain,
% 2.04/2.22 (r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[727, 9544, 272])).
% 2.04/2.22 tff(9546,plain,
% 2.04/2.22 (~r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4123, 9545, 118])).
% 2.04/2.22 tff(9547,plain,
% 2.04/2.22 (b(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2463, 9546, 4645])).
% 2.04/2.22 tff(9548,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2456, 9547, 1659, 9543])).
% 2.04/2.22 tff(9549,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9506, 9545, 3243, 2, 9344, 4102, 118, 4645])).
% 2.04/2.22 tff(9550,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[857, 9549, 853])).
% 2.04/2.22 tff(9551,plain,
% 2.04/2.22 (~r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4119, 9550, 9545])).
% 2.04/2.22 tff(9552,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[921, 9551, 9548, 61])).
% 2.04/2.22 tff(9553,plain,((elem!1 = s(z)) | (~b(s(s(s(z))), z)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9554,plain,
% 2.04/2.22 (elem!1 = s(z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9553, 9482, 853, 4946, 8545, 118, 1301, 50, 1925, 829])).
% 2.04/2.22 tff(9555,plain,
% 2.04/2.22 (b(z, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3403, 9554, 1925])).
% 2.04/2.22 tff(9556,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1795, 9555, 9482, 8545])).
% 2.04/2.22 tff(9557,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1792, 9556])).
% 2.04/2.22 tff(9558,plain,
% 2.04/2.22 (~b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4313, 9555, 1301, 811, 9482])).
% 2.04/2.22 tff(9559,plain,
% 2.04/2.22 (~b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6686, 9558, 9554])).
% 2.04/2.22 tff(9560,plain,
% 2.04/2.22 (r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1759, 9559, 68])).
% 2.04/2.22 tff(9561,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1177, 9560, 9557])).
% 2.04/2.22 tff(9562,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[857, 9561, 853])).
% 2.04/2.22 tff(9563,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3888, 337, 9344, 1301, 8545, 9562, 9555, 9482])).
% 2.04/2.22 tff(9564,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9565,plain,
% 2.04/2.22 (s(s(s(s(z)))) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9564, 8520, 1301, 1925, 118, 50, 829])).
% 2.04/2.22 tff(9566,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9565])).
% 2.04/2.22 tff(9567,plain,
% 2.04/2.22 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(symmetry,[status(thm)],[9566])).
% 2.04/2.22 tff(9568,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9344, 9567])).
% 2.04/2.22 tff(9569,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8519, 9568])).
% 2.04/2.22 tff(9570,plain,(b(s(s(s(s(z)))), s(z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9571,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9570, 8513, 7636, 49, 50, 9343])).
% 2.04/2.22 tff(9572,plain,
% 2.04/2.22 (~(s(s(s(z))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1472, 9343])).
% 2.04/2.22 tff(9573,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7192, 337, 1301, 1275, 1231])).
% 2.04/2.22 tff(9574,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1792, 9573])).
% 2.04/2.22 tff(9575,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8161, 337, 327, 1275, 1231])).
% 2.04/2.22 tff(9576,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[857, 9575, 853])).
% 2.04/2.22 tff(9577,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9578,plain,
% 2.04/2.22 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9579,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9578])).
% 2.04/2.22 tff(9580,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9579, 9577])).
% 2.04/2.22 tff(9581,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9582,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9581, 9580])).
% 2.04/2.22 tff(9583,plain,
% 2.04/2.22 (~b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9582, 337, 327, 1301, 1275, 1231])).
% 2.04/2.22 tff(9584,plain,
% 2.04/2.22 (r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1759, 9583, 1900])).
% 2.04/2.22 tff(9585,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1177, 9584, 9576, 9574])).
% 2.04/2.22 tff(9586,plain,((~b(s(z), s(s(s(s(z)))))) | (elem!1 = z) | (s(s(s(s(z)))) = elem!1) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9587,plain,
% 2.04/2.22 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9586, 853, 1900, 1301, 1231, 327])).
% 2.04/2.22 tff(9588,plain,
% 2.04/2.22 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1150, 9587])).
% 2.04/2.22 tff(9589,plain,
% 2.04/2.22 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[245])).
% 2.04/2.22 tff(9590,plain,
% 2.04/2.22 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.04/2.22 inference(symmetry,[status(thm)],[9589])).
% 2.04/2.22 tff(9591,plain,
% 2.04/2.22 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9590])).
% 2.04/2.22 tff(9592,plain,
% 2.04/2.22 (~b(elem!1, s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[6600, 9591])).
% 2.04/2.22 tff(9593,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[327, 9592])).
% 2.04/2.22 tff(9594,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9595,plain,
% 2.04/2.22 (~(s(z) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9594, 327])).
% 2.04/2.22 tff(9596,plain,
% 2.04/2.22 (~b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3908, 791, 1301, 327])).
% 2.04/2.22 tff(9597,plain,
% 2.04/2.22 (r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1759, 9596, 1900])).
% 2.04/2.22 tff(9598,plain,
% 2.04/2.22 (((~b(elem!1, s(z))) | (~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(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))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9599,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(s(s(s(z)))), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9598])).
% 2.04/2.23 tff(9600,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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(X1, 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(s(s(s(z)))), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9599, 859])).
% 2.04/2.23 tff(9601,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9602,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9601, 9600])).
% 2.04/2.23 tff(9603,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9602, 337, 327, 791, 1231])).
% 2.04/2.23 tff(9604,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[857, 9603, 853])).
% 2.04/2.23 tff(9605,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5594, 337, 327, 791, 1301, 1231])).
% 2.04/2.23 tff(9606,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1792, 9605])).
% 2.04/2.23 tff(9607,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1177, 9606, 9604, 9597])).
% 2.04/2.23 tff(9608,plain,((~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9609,plain,
% 2.04/2.23 (~b(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9608, 853, 327, 1301, 1231, 1900])).
% 2.04/2.23 tff(9610,plain,
% 2.04/2.23 (r(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[727, 9609, 9595])).
% 2.04/2.23 tff(9611,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2089, 1735, 1141])).
% 2.04/2.23 tff(9612,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[857, 9611, 853])).
% 2.04/2.23 tff(9613,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4143, 9612, 9496, 327, 1141, 1735, 4102, 118])).
% 2.04/2.23 tff(9614,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9615,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9614, 9610, 9588, 327, 118, 853, 1481])).
% 2.04/2.23 tff(9616,plain,((s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9617,plain,
% 2.04/2.23 (s(s(s(s(z)))) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9616, 9342, 49, 9572, 8513, 9571, 68])).
% 2.04/2.23 tff(9618,plain,
% 2.04/2.23 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9617])).
% 2.04/2.23 tff(9619,plain,
% 2.04/2.23 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[9618])).
% 2.04/2.23 tff(9620,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[170, 9617, 50])).
% 2.04/2.23 tff(9621,plain,
% 2.04/2.23 (~(s(elem!1) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[264, 9620])).
% 2.04/2.23 tff(9622,plain,
% 2.04/2.23 (~(s(z) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9594, 9342])).
% 2.04/2.23 tff(9623,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9617])).
% 2.04/2.23 tff(9624,plain,
% 2.04/2.23 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9623])).
% 2.04/2.23 tff(9625,plain,
% 2.04/2.23 (~(s(z) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9594, 9344])).
% 2.04/2.23 tff(9626,plain,
% 2.04/2.23 (~r(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2060, 1339, 157, 118])).
% 2.04/2.23 tff(9627,plain,
% 2.04/2.23 (b(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[727, 9626, 9625])).
% 2.04/2.23 tff(9628,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[170, 157, 50])).
% 2.04/2.23 tff(9629,plain,
% 2.04/2.23 (~(s(elem!1) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[264, 9628])).
% 2.04/2.23 tff(9630,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[157])).
% 2.04/2.23 tff(9631,plain,
% 2.04/2.23 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[157])).
% 2.04/2.23 tff(9632,plain,
% 2.04/2.23 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[9631])).
% 2.04/2.23 tff(9633,plain,
% 2.04/2.23 (~b(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4055, 337, 9344, 9627, 1301])).
% 2.04/2.23 tff(9634,plain,
% 2.04/2.23 (r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[921, 9633, 61])).
% 2.04/2.23 tff(9635,plain,
% 2.04/2.23 (r(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9634, 9632])).
% 2.04/2.23 tff(9636,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5133, 9635, 1301, 1339])).
% 2.04/2.23 tff(9637,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2268, 9636])).
% 2.04/2.23 tff(9638,plain,
% 2.04/2.23 (b(s(s(z)), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9637, 9630])).
% 2.04/2.23 tff(9639,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9640,plain,
% 2.04/2.23 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9641,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9640])).
% 2.04/2.23 tff(9642,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9641, 9639])).
% 2.04/2.23 tff(9643,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9644,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9643, 9642])).
% 2.04/2.23 tff(9645,plain,
% 2.04/2.23 (~b(s(z), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9644, 337, 9344, 9627, 9638])).
% 2.04/2.23 tff(9646,plain,
% 2.04/2.23 (r(s(z), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8207, 9645])).
% 2.04/2.23 tff(9647,plain,
% 2.04/2.23 (~b(s(s(z)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2876, 337, 9344, 9627, 9638])).
% 2.04/2.23 tff(9648,plain,
% 2.04/2.23 (r(s(s(z)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2229, 9647])).
% 2.04/2.23 tff(9649,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7348, 189, 118, 9648])).
% 2.04/2.23 tff(9650,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2854, 9649])).
% 2.04/2.23 tff(9651,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1293, 189, 118, 9648])).
% 2.04/2.23 tff(9652,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4268, 9651])).
% 2.04/2.23 tff(9653,plain,
% 2.04/2.23 (~b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7507, 9652, 1339, 9635, 9650])).
% 2.04/2.23 tff(9654,plain,
% 2.04/2.23 ((z = s(s(z))) | r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9005, 43, 9653])).
% 2.04/2.23 tff(9655,plain,
% 2.04/2.23 (r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9654, 9002])).
% 2.04/2.23 tff(9656,plain,
% 2.04/2.23 (~r(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9013, 189, 9655, 9646])).
% 2.04/2.23 tff(9657,plain,
% 2.04/2.23 (b(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[963, 9656])).
% 2.04/2.23 tff(9658,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 2.04/2.23 tff(9659,plain,
% 2.04/2.23 (~b(s(s(z)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2876, 337, 327, 791, 9658])).
% 2.04/2.23 tff(9660,plain,
% 2.04/2.23 (r(s(s(z)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2229, 9659])).
% 2.04/2.23 tff(9661,plain,
% 2.04/2.23 (~b(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7002, 2520, 327, 1, 1301])).
% 2.04/2.23 tff(9662,plain,
% 2.04/2.23 (r(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[898, 9661, 50])).
% 2.04/2.23 tff(9663,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9664,plain,
% 2.04/2.23 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9665,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9664])).
% 2.04/2.23 tff(9666,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9665, 9663])).
% 2.04/2.23 tff(9667,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9668,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9667, 9666])).
% 2.04/2.23 tff(9669,plain,
% 2.04/2.23 (~r(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9668, 189, 9662, 9660])).
% 2.04/2.23 tff(9670,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9671,plain,
% 2.04/2.23 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9672,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9671])).
% 2.04/2.23 tff(9673,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9672, 9670])).
% 2.04/2.23 tff(9674,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9675,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9674, 9673])).
% 2.04/2.23 tff(9676,plain,
% 2.04/2.23 (~b(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9675, 337, 327, 2520, 791, 9658])).
% 2.04/2.23 tff(9677,plain,
% 2.04/2.23 (~(elem!1 = s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9595, 729])).
% 2.04/2.23 tff(9678,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 2.04/2.23 tff(9679,plain,
% 2.04/2.23 (s(s(z)) = s(elem!1)),
% 2.04/2.23 inference(symmetry,[status(thm)],[9678])).
% 2.04/2.23 tff(9680,plain,
% 2.04/2.23 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9679])).
% 2.04/2.23 tff(9681,plain,
% 2.04/2.23 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 2.04/2.23 inference(symmetry,[status(thm)],[9680])).
% 2.04/2.23 tff(9682,plain,
% 2.04/2.23 (elem!1 = s(z)),
% 2.04/2.23 inference(transitivity,[status(thm)],[92, 9681, 104])).
% 2.04/2.23 tff(9683,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[247, 9682])).
% 2.04/2.23 tff(9684,plain,((~(s(elem!1) = s(s(z)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9685,plain,
% 2.04/2.23 (~(s(elem!1) = s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9684, 9677])).
% 2.04/2.23 tff(9686,plain,
% 2.04/2.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9687,plain,
% 2.04/2.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9688,plain,
% 2.04/2.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9687, 9686])).
% 2.04/2.23 tff(9689,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9688, 43, 9685, 9676, 9669])).
% 2.04/2.23 tff(9690,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9691,plain,
% 2.04/2.23 (~b(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9690, 9627, 9344, 9638, 50, 9657, 1301])).
% 2.04/2.23 tff(9692,plain,
% 2.04/2.23 (r(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[270, 9691, 9629])).
% 2.04/2.23 tff(9693,plain,
% 2.04/2.23 (~(elem!1 = s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9625, 729])).
% 2.04/2.23 tff(9694,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[801, 157, 9693])).
% 2.04/2.23 tff(9695,plain,
% 2.04/2.23 (~r(z, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1748, 9692, 9634])).
% 2.04/2.23 tff(9696,plain,
% 2.04/2.23 (b(z, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[395, 9695])).
% 2.04/2.23 tff(9697,plain,
% 2.04/2.23 (~r(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9537, 9696, 1925, 9344, 9628, 9694, 9627, 61, 9692])).
% 2.04/2.23 tff(9698,plain,
% 2.04/2.23 (b(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[898, 9697, 50])).
% 2.04/2.23 tff(9699,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9700,plain,
% 2.04/2.23 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9701,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9700])).
% 2.04/2.23 tff(9702,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9701, 9699])).
% 2.04/2.23 tff(9703,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9704,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9703, 9702])).
% 2.04/2.23 tff(9705,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9704, 337, 9344, 9696, 9698, 9627, 1301])).
% 2.04/2.23 tff(9706,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9707,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9706, 8513, 50, 7636, 49, 9617])).
% 2.04/2.23 tff(9708,plain,
% 2.04/2.23 (~r(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9707, 9624])).
% 2.04/2.23 tff(9709,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), elem!1) <=> b(elem!1, elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9617])).
% 2.04/2.23 tff(9710,plain,
% 2.04/2.23 (b(elem!1, elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(symmetry,[status(thm)],[9709])).
% 2.04/2.23 tff(9711,plain,
% 2.04/2.23 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9710])).
% 2.04/2.23 tff(9712,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[6600, 9711])).
% 2.04/2.23 tff(9713,plain,
% 2.04/2.23 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[427, 9620])).
% 2.04/2.23 tff(9714,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9617])).
% 2.04/2.23 tff(9715,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[548, 9707])).
% 2.04/2.23 tff(9716,plain,
% 2.04/2.23 (b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9715, 9714])).
% 2.04/2.23 tff(9717,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2510, 9617, 50])).
% 2.04/2.23 tff(9718,plain,
% 2.04/2.23 (~r(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2896, 275, 1735])).
% 2.04/2.23 tff(9719,plain,
% 2.04/2.23 (b(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1759, 9718, 3768])).
% 2.04/2.23 tff(9720,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2456, 9719, 3929, 2454, 8888])).
% 2.04/2.23 tff(9721,plain,((~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (z = elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9722,plain,
% 2.04/2.23 (~r(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9721, 1735, 61, 2454, 118])).
% 2.04/2.23 tff(9723,plain,
% 2.04/2.23 (b(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[963, 9722])).
% 2.04/2.23 tff(9724,plain,
% 2.04/2.23 (~b(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[970, 337, 9344, 9723, 1301])).
% 2.04/2.23 tff(9725,plain,
% 2.04/2.23 (r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[921, 9724, 61])).
% 2.04/2.23 tff(9726,plain,
% 2.04/2.23 (~r(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6190, 9725, 50, 1301, 1735])).
% 2.04/2.23 tff(9727,plain,
% 2.04/2.23 (b(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[270, 9726, 978])).
% 2.04/2.23 tff(9728,plain,
% 2.04/2.23 (~b(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7002, 9727, 9344, 9723, 1301])).
% 2.04/2.23 tff(9729,plain,
% 2.04/2.23 (r(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[898, 9728, 50])).
% 2.04/2.23 tff(9730,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4845, 189, 9729, 118])).
% 2.04/2.23 tff(9731,plain,
% 2.04/2.23 (~b(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9353, 337, 9344, 1925, 9723, 1301])).
% 2.04/2.23 tff(9732,plain,
% 2.04/2.23 (r(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1759, 9731, 68])).
% 2.04/2.23 tff(9733,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8725, 1735, 1925, 6583, 61])).
% 2.04/2.23 tff(9734,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9735,plain,
% 2.04/2.23 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(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(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(9736,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9735])).
% 2.04/2.23 tff(9737,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, 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), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[9736, 9734])).
% 2.04/2.23 tff(9738,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(9739,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9738, 9737])).
% 2.04/2.23 tff(9740,plain,
% 2.04/2.23 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9739, 337, 9733, 2520, 982])).
% 2.04/2.23 tff(9741,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4119, 1735, 7994])).
% 2.04/2.23 tff(9742,plain,
% 2.04/2.23 (s(s(s(s(z)))) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[857, 9741, 229])).
% 2.04/2.23 tff(9743,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2510, 9742, 50])).
% 2.04/2.23 tff(9744,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[9742])).
% 2.04/2.23 tff(9745,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8251, 9742, 2461])).
% 2.04/2.23 tff(9746,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[548, 9745])).
% 2.04/2.23 tff(9747,plain,
% 2.04/2.23 (b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[9746, 9744])).
% 2.04/2.23 tff(9748,plain,
% 2.04/2.23 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5886, 9747, 2451, 9733, 2520, 982, 9743])).
% 2.04/2.23 tff(9749,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[579, 9748, 9740, 983])).
% 2.04/2.23 tff(9750,plain,((~r(s(z), elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | r(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), elem!1) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(9751,plain,
% 2.04/2.23 (~b(elem!1, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9750, 9727, 1925, 983, 229, 50, 1735, 2461, 9724])).
% 2.04/2.23 tff(9752,plain,
% 2.04/2.23 (r(elem!1, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1015, 9751, 3146])).
% 2.04/2.24 tff(9753,plain,
% 2.04/2.24 (~r(s(elem!1), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1023, 9752, 9732])).
% 2.04/2.24 tff(9754,plain,
% 2.04/2.24 (b(s(elem!1), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[378, 43, 114, 9753])).
% 2.04/2.24 tff(9755,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9756,plain,
% 2.04/2.24 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9757,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9756])).
% 2.04/2.24 tff(9758,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9757, 9755])).
% 2.04/2.24 tff(9759,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(9760,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9759, 9758])).
% 2.04/2.24 tff(9761,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9760, 337, 9344, 9727, 9723, 9754, 2454])).
% 2.04/2.24 tff(9762,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 9761, 9730])).
% 2.04/2.24 tff(9763,plain,((~r(s(z), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1) | (~b(z, s(z))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9764,plain,
% 2.04/2.24 (~r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9763, 9717, 9716, 49, 50, 7636, 9713, 9712, 9708, 8513, 9621])).
% 2.04/2.24 tff(9765,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[727, 9764, 9622])).
% 2.04/2.24 tff(9766,plain,
% 2.04/2.24 (~b(z, elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4055, 337, 9342, 9765, 8513])).
% 2.04/2.24 tff(9767,plain,
% 2.04/2.24 (r(z, elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[921, 9766, 61])).
% 2.04/2.24 tff(9768,plain,
% 2.04/2.24 (~(elem!1 = s(z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9622, 729])).
% 2.04/2.24 tff(9769,plain,
% 2.04/2.24 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[801, 9617, 9768])).
% 2.04/2.24 tff(9770,plain,
% 2.04/2.24 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5465, 326, 2470, 327, 2454, 791])).
% 2.04/2.24 tff(9771,plain,
% 2.04/2.24 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1979, 326, 327, 791])).
% 2.04/2.24 tff(9772,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1970, 9771, 9770])).
% 2.04/2.24 tff(9773,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9774,plain,
% 2.04/2.24 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9773, 9342, 9765, 2451, 9716])).
% 2.04/2.24 tff(9775,plain,
% 2.04/2.24 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[350, 9774, 9769])).
% 2.04/2.24 tff(9776,plain,
% 2.04/2.24 (~r(s(elem!1), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[765, 9775, 9620, 9767])).
% 2.04/2.24 tff(9777,plain,
% 2.04/2.24 (b(s(elem!1), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[270, 9776, 9621])).
% 2.04/2.24 tff(9778,plain,
% 2.04/2.24 (b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9777, 9619])).
% 2.04/2.24 tff(9779,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5643, 9765, 9617])).
% 2.04/2.24 tff(9780,plain,
% 2.04/2.24 (~b(s(elem!1), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2592, 337, 9342, 9777, 9765])).
% 2.04/2.24 tff(9781,plain,
% 2.04/2.24 (r(s(elem!1), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[898, 9780, 50])).
% 2.04/2.24 tff(9782,plain,
% 2.04/2.24 (~b(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4847, 9781, 9717, 9715, 9779, 9571, 9778])).
% 2.04/2.24 tff(9783,plain,
% 2.04/2.24 (r(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[963, 9782])).
% 2.04/2.24 tff(9784,plain,
% 2.04/2.24 (~b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3908, 9765, 8513, 9342])).
% 2.04/2.24 tff(9785,plain,
% 2.04/2.24 (r(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1759, 9784, 68])).
% 2.04/2.24 tff(9786,plain,
% 2.04/2.24 (~r(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3859, 9783, 9785])).
% 2.04/2.24 tff(9787,plain,
% 2.04/2.24 (~b(z, s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5667, 9786, 8513, 9712, 9764, 50, 9785, 9343, 49, 9768, 9777])).
% 2.04/2.24 tff(9788,plain,
% 2.04/2.24 (r(z, s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[395, 9787])).
% 2.04/2.24 tff(9789,plain,
% 2.04/2.24 (~r(s(z), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6246, 9788, 9783])).
% 2.04/2.24 tff(9790,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9791,plain,
% 2.04/2.24 (((~b(s(z), elem!1)) | (~b(s(elem!1), 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(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9792,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), 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(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9791])).
% 2.04/2.24 tff(9793,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), 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(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9792, 9790])).
% 2.04/2.24 tff(9794,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(9795,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9794, 9793])).
% 2.04/2.24 tff(9796,plain,
% 2.04/2.24 (~b(s(z), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9795, 337, 9342, 9777, 9765])).
% 2.04/2.24 tff(9797,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2133, 43, 9796, 9789, 55])).
% 2.04/2.24 tff(9798,plain,((s(elem!1) = s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9799,plain,
% 2.04/2.24 (s(elem!1) = s(z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9798, 3])).
% 2.04/2.24 tff(9800,plain,
% 2.04/2.24 (z = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3076, 9799])).
% 2.04/2.24 tff(9801,plain,
% 2.04/2.24 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9799])).
% 2.04/2.24 tff(9802,plain,
% 2.04/2.24 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.24 inference(symmetry,[status(thm)],[9801])).
% 2.04/2.24 tff(9803,plain,
% 2.04/2.24 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9800])).
% 2.04/2.24 tff(9804,plain,
% 2.04/2.24 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.04/2.24 inference(transitivity,[status(thm)],[9803, 9802])).
% 2.04/2.24 tff(9805,plain,
% 2.04/2.24 (b(s(elem!1), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[1, 9804])).
% 2.04/2.24 tff(9806,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[1, 9803])).
% 2.04/2.24 tff(9807,plain,
% 2.04/2.24 (s(s(elem!1)) = s(s(z))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[3070])).
% 2.04/2.24 tff(9808,plain,
% 2.04/2.24 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9807])).
% 2.04/2.24 tff(9809,plain,
% 2.04/2.24 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[9808])).
% 2.04/2.24 tff(9810,plain,
% 2.04/2.24 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9809])).
% 2.04/2.24 tff(9811,plain,
% 2.04/2.24 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[9810])).
% 2.04/2.24 tff(9812,plain,
% 2.04/2.24 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[3070])).
% 2.04/2.24 tff(9813,plain,
% 2.04/2.24 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9812, 9811])).
% 2.04/2.24 tff(9814,plain,
% 2.04/2.24 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[423])).
% 2.04/2.24 tff(9815,plain,
% 2.04/2.24 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[3070])).
% 2.04/2.24 tff(9816,plain,
% 2.04/2.24 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9815, 366])).
% 2.04/2.24 tff(9817,plain,
% 2.04/2.24 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.24 inference(symmetry,[status(thm)],[9816])).
% 2.04/2.24 tff(9818,plain,
% 2.04/2.24 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9817, 9814])).
% 2.04/2.24 tff(9819,plain,
% 2.04/2.24 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9818])).
% 2.04/2.24 tff(9820,plain,
% 2.04/2.24 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[211, 9819])).
% 2.04/2.24 tff(9821,plain,
% 2.04/2.24 (z = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3076, 3070])).
% 2.04/2.24 tff(9822,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9821])).
% 2.04/2.24 tff(9823,plain,
% 2.04/2.24 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9822])).
% 2.04/2.24 tff(9824,plain,
% 2.04/2.24 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[817, 9823])).
% 2.04/2.24 tff(9825,plain,
% 2.04/2.24 (elem!1 = z),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4411, 9821])).
% 2.04/2.24 tff(9826,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.24 tff(9827,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9826, 2114])).
% 2.04/2.24 tff(9828,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.24 inference(transitivity,[status(thm)],[9827, 2115])).
% 2.04/2.24 tff(9829,plain,
% 2.04/2.24 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9828])).
% 2.04/2.24 tff(9830,plain,
% 2.04/2.24 (~(s(s(z)) = elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[31, 9829])).
% 2.04/2.24 tff(9831,plain,
% 2.04/2.24 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.24 tff(9832,plain,
% 2.04/2.24 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.04/2.24 inference(symmetry,[status(thm)],[9831])).
% 2.04/2.24 tff(9833,plain,
% 2.04/2.24 (b(s(z), z)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[791, 9832])).
% 2.04/2.24 tff(9834,plain,
% 2.04/2.24 (~b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7799, 9833, 118, 173])).
% 2.04/2.24 tff(9835,plain,
% 2.04/2.24 (r(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1786, 9834])).
% 2.04/2.24 tff(9836,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8078, 9835, 173])).
% 2.04/2.24 tff(9837,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[851, 9836])).
% 2.04/2.24 tff(9838,plain,
% 2.04/2.24 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1580, 9835, 173])).
% 2.04/2.24 tff(9839,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1150, 9838])).
% 2.04/2.24 tff(9840,plain,
% 2.04/2.24 (~r(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2253, 2821, 173])).
% 2.04/2.24 tff(9841,plain,
% 2.04/2.24 (r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8207, 1422])).
% 2.04/2.24 tff(9842,plain,
% 2.04/2.24 (~b(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8213, 9841, 118, 173])).
% 2.04/2.24 tff(9843,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2242, 9842, 9840])).
% 2.04/2.24 tff(9844,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9845,plain,
% 2.04/2.24 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9844, 9839, 173, 118, 9837, 791])).
% 2.04/2.24 tff(9846,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2268, 9845])).
% 2.04/2.24 tff(9847,plain,
% 2.04/2.24 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.24 tff(9848,plain,
% 2.04/2.24 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[9847])).
% 2.04/2.24 tff(9849,plain,
% 2.04/2.24 (b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4942, 9848])).
% 2.04/2.24 tff(9850,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1784, 9849])).
% 2.04/2.24 tff(9851,plain,((~b(elem!1, s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9852,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9851, 9834, 56])).
% 2.04/2.24 tff(9853,plain,
% 2.04/2.24 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(commutativity,[status(thm)],[])).
% 2.04/2.24 tff(9854,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[9853])).
% 2.04/2.24 tff(9855,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.24 tff(9856,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9855, 9854])).
% 2.04/2.24 tff(9857,plain,
% 2.04/2.24 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9856])).
% 2.04/2.24 tff(9858,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[817, 9857])).
% 2.04/2.24 tff(9859,plain,
% 2.04/2.24 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2845, 43, 9858, 9852])).
% 2.04/2.24 tff(9860,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2849, 189, 9859, 9846])).
% 2.04/2.24 tff(9861,plain,
% 2.04/2.24 (b(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2301, 9860, 9830])).
% 2.04/2.24 tff(9862,plain,
% 2.04/2.24 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9827])).
% 2.04/2.24 tff(9863,plain,
% 2.04/2.24 (~(elem!1 = s(s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[31, 9862])).
% 2.04/2.24 tff(9864,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9865,plain,
% 2.04/2.24 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9866,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9865])).
% 2.04/2.24 tff(9867,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9866, 9864])).
% 2.04/2.24 tff(9868,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(9869,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9868, 9867])).
% 2.04/2.24 tff(9870,plain,
% 2.04/2.24 (~r(elem!1, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9869, 189, 9859, 9846])).
% 2.04/2.24 tff(9871,plain,
% 2.04/2.24 (b(elem!1, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9064, 9870, 9863])).
% 2.04/2.24 tff(9872,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9873,plain,
% 2.04/2.24 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(9874,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9873])).
% 2.04/2.24 tff(9875,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9874, 9872])).
% 2.04/2.24 tff(9876,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(9877,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9876, 9875])).
% 2.04/2.24 tff(9878,plain,
% 2.04/2.24 (~b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9877, 337, 791, 9871, 9861])).
% 2.04/2.24 tff(9879,plain,
% 2.04/2.24 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.24 tff(9880,plain,
% 2.04/2.24 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.04/2.24 inference(symmetry,[status(thm)],[9879])).
% 2.04/2.24 tff(9881,plain,
% 2.04/2.24 (b(s(s(z)), z)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[9861, 9880])).
% 2.04/2.24 tff(9882,plain,
% 2.04/2.24 (~r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8213, 9881, 118, 173])).
% 2.04/2.24 tff(9883,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8207, 9882, 9878])).
% 2.04/2.24 tff(9884,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9885,plain,
% 2.04/2.24 (~r(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9884, 791, 118, 9821])).
% 2.04/2.24 tff(9886,plain,
% 2.04/2.24 (b(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[80, 9885])).
% 2.04/2.24 tff(9887,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4863, 9886, 9825])).
% 2.04/2.24 tff(9888,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1570, 337, 327, 791, 1275, 1603])).
% 2.04/2.24 tff(9889,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(9890,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9889, 1275, 791, 9887])).
% 2.04/2.24 tff(9891,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[857, 9890, 9824])).
% 2.04/2.24 tff(9892,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9821])).
% 2.04/2.24 tff(9893,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[9892, 2114])).
% 2.04/2.24 tff(9894,plain,
% 2.04/2.24 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.24 inference(transitivity,[status(thm)],[9893, 2115])).
% 2.04/2.24 tff(9895,plain,
% 2.04/2.24 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[9894])).
% 2.04/2.24 tff(9896,plain,
% 2.04/2.24 (~(s(s(z)) = elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[31, 9895])).
% 2.04/2.24 tff(9897,plain,
% 2.04/2.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1198, 189, 811, 2245])).
% 2.04/2.24 tff(9898,plain,
% 2.04/2.24 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2268, 9897])).
% 2.04/2.24 tff(9899,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4265, 337, 4946, 2, 9898, 8599])).
% 2.04/2.24 tff(9900,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(9901,plain,
% 2.04/2.25 (~r(s(s(z)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9900, 811, 118, 2])).
% 2.04/2.25 tff(9902,plain,
% 2.04/2.25 (b(s(s(z)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2229, 9901])).
% 2.04/2.25 tff(9903,plain,
% 2.04/2.25 (~b(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4234, 337, 327, 791, 9902])).
% 2.04/2.25 tff(9904,plain,
% 2.04/2.25 (r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2301, 9903, 4103])).
% 2.04/2.25 tff(9905,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~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)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9906,plain,
% 2.04/2.25 (((~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(s(s(z)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9907,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9906])).
% 2.04/2.25 tff(9908,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9907, 9905])).
% 2.04/2.25 tff(9909,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9910,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9909, 9908])).
% 2.04/2.25 tff(9911,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9910, 189, 1169, 9904])).
% 2.04/2.25 tff(9912,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2268, 9911])).
% 2.04/2.25 tff(9913,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8199, 337, 4946, 1275, 2, 9912, 9902])).
% 2.04/2.25 tff(9914,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(9915,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9914, 1169, 2, 1275, 9896, 9887, 791, 118])).
% 2.04/2.25 tff(9916,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[851, 9915])).
% 2.04/2.25 tff(9917,plain,
% 2.04/2.25 (~b(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4234, 337, 327, 791, 3357])).
% 2.04/2.25 tff(9918,plain,
% 2.04/2.25 (r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2301, 9917, 4103])).
% 2.04/2.25 tff(9919,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9920,plain,
% 2.04/2.25 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9921,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9920])).
% 2.04/2.25 tff(9922,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9921, 9919])).
% 2.04/2.25 tff(9923,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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)))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9924,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9923, 9922])).
% 2.04/2.25 tff(9925,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9924, 337, 327, 791, 1231, 3357])).
% 2.04/2.25 tff(9926,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2268, 9925])).
% 2.04/2.25 tff(9927,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9910, 189, 1169, 9926, 9918])).
% 2.04/2.25 tff(9928,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(9929,plain,
% 2.04/2.25 (~b(s(s(z)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9928, 1169, 9896, 9887, 791, 9916])).
% 2.04/2.25 tff(9930,plain,
% 2.04/2.25 (r(s(s(z)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2229, 9929])).
% 2.04/2.25 tff(9931,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1293, 189, 118, 9930])).
% 2.04/2.25 tff(9932,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4268, 9931])).
% 2.04/2.25 tff(9933,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9934,plain,
% 2.04/2.25 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9935,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(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(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9934])).
% 2.04/2.25 tff(9936,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(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(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9935, 9933])).
% 2.04/2.25 tff(9937,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9938,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9937, 9936])).
% 2.04/2.25 tff(9939,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9938, 337, 1275, 2, 1231, 1396, 7403])).
% 2.04/2.25 tff(9940,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(9941,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9940, 9916, 2, 1275, 9932])).
% 2.04/2.25 tff(9942,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2268, 9941])).
% 2.04/2.25 tff(9943,plain,
% 2.04/2.25 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9821])).
% 2.04/2.25 tff(9944,plain,
% 2.04/2.25 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9943, 3256])).
% 2.04/2.25 tff(9945,plain,
% 2.04/2.25 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9944])).
% 2.04/2.25 tff(9946,plain,
% 2.04/2.25 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[659, 9945])).
% 2.04/2.25 tff(9947,plain,
% 2.04/2.25 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[3070])).
% 2.04/2.25 tff(9948,plain,
% 2.04/2.25 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[9947])).
% 2.04/2.25 tff(9949,plain,
% 2.04/2.25 (b(elem!1, s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9887, 9948])).
% 2.04/2.25 tff(9950,plain,
% 2.04/2.25 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9808])).
% 2.04/2.25 tff(9951,plain,
% 2.04/2.25 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9950, 3070])).
% 2.04/2.25 tff(9952,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[9951])).
% 2.04/2.25 tff(9953,plain,
% 2.04/2.25 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9916, 9952])).
% 2.04/2.25 tff(9954,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3580, 9953, 2520, 9949])).
% 2.04/2.25 tff(9955,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3274, 9954, 9946])).
% 2.04/2.25 tff(9956,plain,
% 2.04/2.25 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9809])).
% 2.04/2.25 tff(9957,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9950])).
% 2.04/2.25 tff(9958,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9955, 9957])).
% 2.04/2.25 tff(9959,plain,
% 2.04/2.25 (~r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2849, 189, 9958, 9942])).
% 2.04/2.25 tff(9960,plain,
% 2.04/2.25 (b(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2301, 9959, 9896])).
% 2.04/2.25 tff(9961,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9962,plain,
% 2.04/2.25 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9963,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9962])).
% 2.04/2.25 tff(9964,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9963, 9961])).
% 2.04/2.25 tff(9965,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9966,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9965, 9964])).
% 2.04/2.25 tff(9967,plain,
% 2.04/2.25 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9966, 337, 9887, 2, 9916, 9932])).
% 2.04/2.25 tff(9968,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9967, 9960])).
% 2.04/2.25 tff(9969,plain,
% 2.04/2.25 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9821])).
% 2.04/2.25 tff(9970,plain,
% 2.04/2.25 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9969, 5931])).
% 2.04/2.25 tff(9971,plain,
% 2.04/2.25 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9970])).
% 2.04/2.25 tff(9972,plain,
% 2.04/2.25 (~(elem!1 = s(s(s(z))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[178, 9971])).
% 2.04/2.25 tff(9973,plain,
% 2.04/2.25 (r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5966, 43, 9972, 9968])).
% 2.04/2.25 tff(9974,plain,
% 2.04/2.25 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9973, 9956])).
% 2.04/2.25 tff(9975,plain,
% 2.04/2.25 (s(s(z)) = s(s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[57])).
% 2.04/2.25 tff(9976,plain,
% 2.04/2.25 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9975])).
% 2.04/2.25 tff(9977,plain,
% 2.04/2.25 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.25 inference(symmetry,[status(thm)],[9976])).
% 2.04/2.25 tff(9978,plain,
% 2.04/2.25 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9976])).
% 2.04/2.25 tff(9979,plain,
% 2.04/2.25 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[9978])).
% 2.04/2.25 tff(9980,plain,
% 2.04/2.25 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9979, 9977])).
% 2.04/2.25 tff(9981,plain,
% 2.04/2.25 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[9980])).
% 2.04/2.25 tff(9982,plain,
% 2.04/2.25 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[6489, 9981])).
% 2.04/2.25 tff(9983,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9984,plain,
% 2.04/2.25 (((~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9985,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9984])).
% 2.04/2.25 tff(9986,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9985, 9983])).
% 2.04/2.25 tff(9987,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9988,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9987, 9986])).
% 2.04/2.25 tff(9989,plain,
% 2.04/2.25 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9988, 189, 3277, 283])).
% 2.04/2.25 tff(9990,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9989, 9982])).
% 2.04/2.25 tff(9991,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(9992,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9991, 9974, 9955, 9821])).
% 2.04/2.25 tff(9993,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[524, 9992])).
% 2.04/2.25 tff(9994,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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(X1, 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(z))))) | (~b(s(s(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))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9995,plain,
% 2.04/2.25 (((~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(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(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(9996,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(z))))) | (~b(s(s(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)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[9995])).
% 2.04/2.25 tff(9997,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(z))))) | (~b(s(s(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))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[9996, 9994])).
% 2.04/2.25 tff(9998,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(9999,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(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)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[9998, 9997])).
% 2.04/2.26 tff(10000,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[9999, 337, 3243, 1275, 2, 3242])).
% 2.04/2.26 tff(10001,plain,
% 2.04/2.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(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(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10002,plain,
% 2.04/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10003,plain,
% 2.04/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10002, 10001])).
% 2.04/2.26 tff(10004,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 10000])).
% 2.04/2.26 tff(10005,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 2.04/2.26 tff(10006,plain,
% 2.04/2.26 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10005])).
% 2.04/2.26 tff(10007,plain,
% 2.04/2.26 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[10006])).
% 2.04/2.26 tff(10008,plain,
% 2.04/2.26 (s(s(z)) = s(s(s(s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[21, 10007, 2326])).
% 2.04/2.26 tff(10009,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2263, 10008])).
% 2.04/2.26 tff(10010,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10011,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6709, 3250, 10010])).
% 2.04/2.26 tff(10012,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10013,plain,
% 2.04/2.26 (((~r(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(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10014,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10013])).
% 2.04/2.26 tff(10015,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10014, 10012])).
% 2.04/2.26 tff(10016,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10017,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10016, 10015])).
% 2.04/2.26 tff(10018,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10017, 189, 10011, 6479, 10004])).
% 2.04/2.26 tff(10019,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), 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))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10020,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10019, 9993, 6479, 2, 1275])).
% 2.04/2.26 tff(10021,plain,
% 2.04/2.26 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7877])).
% 2.04/2.26 tff(10022,plain,
% 2.04/2.26 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10021])).
% 2.04/2.26 tff(10023,plain,
% 2.04/2.26 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[10022])).
% 2.04/2.26 tff(10024,plain,
% 2.04/2.26 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[2327, 10023, 161])).
% 2.04/2.26 tff(10025,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[519, 10024])).
% 2.04/2.26 tff(10026,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10027,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6726, 10026])).
% 2.04/2.26 tff(10028,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10027, 10020])).
% 2.04/2.26 tff(10029,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3566, 189, 10028, 9942])).
% 2.04/2.26 tff(10030,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 2.04/2.26 tff(10031,plain,
% 2.04/2.26 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10030])).
% 2.04/2.26 tff(10032,plain,
% 2.04/2.26 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[10031])).
% 2.04/2.26 tff(10033,plain,
% 2.04/2.26 (s(z) = s(s(s(s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[105, 10032, 2326])).
% 2.04/2.26 tff(10034,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[516, 10033])).
% 2.04/2.26 tff(10035,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10036,plain,
% 2.04/2.26 (((~![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))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10037,plain,
% 2.04/2.26 ((~![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))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10038,plain,
% 2.04/2.26 ((~![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)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10037, 10036])).
% 2.04/2.26 tff(10039,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 10029])).
% 2.04/2.26 tff(10040,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.26 inference(commutativity,[status(thm)],[])).
% 2.04/2.26 tff(10041,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[10040])).
% 2.04/2.26 tff(10042,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[9821])).
% 2.04/2.26 tff(10043,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10042, 10040])).
% 2.04/2.26 tff(10044,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(transitivity,[status(thm)],[10043, 10041])).
% 2.04/2.26 tff(10045,plain,
% 2.04/2.26 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10044])).
% 2.04/2.26 tff(10046,plain,
% 2.04/2.26 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10047,plain,
% 2.04/2.26 (~(s(s(s(s(s(z))))) = z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10046, 29])).
% 2.04/2.26 tff(10048,plain,
% 2.04/2.26 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10047, 10045])).
% 2.04/2.26 tff(10049,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10050,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10051,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10050, 10049])).
% 2.04/2.26 tff(10052,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10051, 189, 9958, 10028])).
% 2.04/2.26 tff(10053,plain,
% 2.04/2.26 (((~![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))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10054,plain,
% 2.04/2.26 ((~![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))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10055,plain,
% 2.04/2.26 ((~![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)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10054, 10053])).
% 2.04/2.26 tff(10056,plain,
% 2.04/2.26 ((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)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10055, 43])).
% 2.04/2.26 tff(10057,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10056, 10052, 10048])).
% 2.04/2.26 tff(10058,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10059,plain,
% 2.04/2.26 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10060,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~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(X1, 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(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10059])).
% 2.04/2.26 tff(10061,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~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(X1, 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(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10060, 10058])).
% 2.04/2.26 tff(10062,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10063,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10062, 10061])).
% 2.04/2.26 tff(10064,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10063, 337, 9887, 791, 9960, 10057, 10039])).
% 2.04/2.26 tff(10065,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10066,plain,
% 2.04/2.26 (~r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10065, 9891, 791, 2, 1275, 3070, 118, 2520])).
% 2.04/2.26 tff(10067,plain,
% 2.04/2.26 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[9809])).
% 2.04/2.26 tff(10068,plain,
% 2.04/2.26 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[10067])).
% 2.04/2.26 tff(10069,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[3070])).
% 2.04/2.26 tff(10070,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10069, 10068])).
% 2.04/2.26 tff(10071,plain,
% 2.04/2.26 (r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1113, 10070])).
% 2.04/2.26 tff(10072,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 2.04/2.26 tff(10073,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10072, 10071])).
% 2.04/2.26 tff(10074,plain,((~r(s(elem!1), s(s(s(elem!1))))) | r(s(z), s(s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10075,plain,
% 2.04/2.26 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10074, 10066, 3070])).
% 2.04/2.26 tff(10076,plain,
% 2.04/2.26 (b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[579, 10075, 9820])).
% 2.04/2.26 tff(10077,plain,
% 2.04/2.26 (b(s(z), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10076, 9813])).
% 2.04/2.26 tff(10078,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[9914, 9891, 2, 1275, 9896, 9887, 791, 118])).
% 2.04/2.26 tff(10079,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[851, 10078])).
% 2.04/2.26 tff(10080,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10081,plain,
% 2.04/2.26 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(z), s(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(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10082,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10081])).
% 2.04/2.26 tff(10083,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10082, 10080])).
% 2.04/2.26 tff(10084,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10085,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10084, 10083])).
% 2.04/2.26 tff(10086,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10085, 337, 1275, 2, 10079, 10077])).
% 2.04/2.26 tff(10087,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(s(elem!1) = s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(10088,plain,
% 2.04/2.26 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10087, 9799, 2, 9806, 49, 9805])).
% 2.04/2.26 tff(10089,plain,
% 2.04/2.26 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1150, 10088])).
% 2.04/2.26 tff(10090,plain,
% 2.04/2.26 (elem!1 = z),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4411, 56])).
% 2.04/2.26 tff(10091,plain,
% 2.04/2.26 (~r(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[9884, 791, 118, 56])).
% 2.04/2.26 tff(10092,plain,
% 2.04/2.26 (b(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[80, 10091])).
% 2.04/2.26 tff(10093,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4863, 10092, 10090])).
% 2.04/2.26 tff(10094,plain,
% 2.04/2.26 (~b(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4234, 337, 10093, 791, 9902])).
% 2.04/2.26 tff(10095,plain,
% 2.04/2.26 (r(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2301, 10094, 9830])).
% 2.04/2.26 tff(10096,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[9855])).
% 2.04/2.26 tff(10097,plain,
% 2.04/2.26 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[817, 10096])).
% 2.04/2.26 tff(10098,plain,
% 2.04/2.26 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.26 tff(10099,plain,
% 2.04/2.26 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10098])).
% 2.04/2.26 tff(10100,plain,
% 2.04/2.26 (~(s(s(s(z))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[178, 10099])).
% 2.04/2.26 tff(10101,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4863, 1301, 10090])).
% 2.04/2.26 tff(10102,plain,
% 2.04/2.26 (~b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4287, 1603, 791, 10101, 2])).
% 2.04/2.26 tff(10103,plain,
% 2.04/2.26 (r(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2463, 10102, 10100])).
% 2.04/2.26 tff(10104,plain,
% 2.04/2.26 (~b(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4234, 337, 10101, 791, 3357])).
% 2.04/2.26 tff(10105,plain,
% 2.04/2.26 (r(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2301, 10104, 9830])).
% 2.04/2.26 tff(10106,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10107,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10108,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[10107, 10106])).
% 2.04/2.26 tff(10109,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[10108, 189, 10105, 10103])).
% 2.04/2.26 tff(10110,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2854, 10109])).
% 2.04/2.26 tff(10111,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10112,plain,
% 2.04/2.26 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(10113,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[10112])).
% 2.04/2.26 tff(10114,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[10113, 10111])).
% 2.04/2.26 tff(10115,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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)))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(10116,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))), elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10115, 10114])).
% 2.04/2.27 tff(10117,plain,
% 2.04/2.27 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10116, 337, 10101, 2, 1603, 3357])).
% 2.04/2.27 tff(10118,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10117, 10110])).
% 2.04/2.27 tff(10119,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2268, 10118])).
% 2.04/2.27 tff(10120,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3566, 189, 7908, 4222])).
% 2.04/2.27 tff(10121,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 10120])).
% 2.04/2.27 tff(10122,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10123,plain,
% 2.04/2.27 (((~r(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(z)))) <=> ((~r(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(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10124,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10123])).
% 2.04/2.27 tff(10125,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10124, 10122])).
% 2.04/2.27 tff(10126,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10127,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10126, 10125])).
% 2.04/2.27 tff(10128,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10127, 189, 1141, 7908])).
% 2.04/2.27 tff(10129,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 10128])).
% 2.04/2.27 tff(10130,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10131,plain,
% 2.04/2.27 (((~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)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10132,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10131])).
% 2.04/2.27 tff(10133,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10132, 10130])).
% 2.04/2.27 tff(10134,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10135,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10134, 10133])).
% 2.04/2.27 tff(10136,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10135, 189, 1141, 3370, 4222])).
% 2.04/2.27 tff(10137,plain,((~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,[]))).
% 2.04/2.27 tff(10138,plain,
% 2.04/2.27 (~r(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10137, 1141, 4222])).
% 2.04/2.27 tff(10139,plain,
% 2.04/2.27 (b(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8207, 10138])).
% 2.04/2.27 tff(10140,plain,
% 2.04/2.27 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[7355])).
% 2.04/2.27 tff(10141,plain,
% 2.04/2.27 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10035, 10140])).
% 2.04/2.27 tff(10142,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3299, 10141])).
% 2.04/2.27 tff(10143,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10142, 7922])).
% 2.04/2.27 tff(10144,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(z))) | (~b(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(X1, 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(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10145,plain,
% 2.04/2.27 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10146,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(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(X1, 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(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10145])).
% 2.04/2.27 tff(10147,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(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(X1, 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(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10146, 10144])).
% 2.04/2.27 tff(10148,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10149,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10148, 10147])).
% 2.04/2.27 tff(10150,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10149, 337, 10143, 10139, 3357, 10129, 10121])).
% 2.04/2.27 tff(10151,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(10152,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10151, 10119, 1141, 3357])).
% 2.04/2.27 tff(10153,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10027, 10152])).
% 2.04/2.27 tff(10154,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3249, 337, 3243, 2, 10153])).
% 2.04/2.27 tff(10155,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6709, 10010])).
% 2.04/2.27 tff(10156,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10155, 10154])).
% 2.04/2.27 tff(10157,plain,
% 2.04/2.27 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.27 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.27 tff(10158,plain,
% 2.04/2.27 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10157, 10040])).
% 2.04/2.27 tff(10159,plain,
% 2.04/2.27 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.27 inference(transitivity,[status(thm)],[10158, 10041])).
% 2.04/2.27 tff(10160,plain,
% 2.04/2.27 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10159])).
% 2.04/2.27 tff(10161,plain,
% 2.04/2.27 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10047, 10160])).
% 2.04/2.27 tff(10162,plain,
% 2.04/2.27 (~r(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4348, 10119, 1301, 791, 10101, 1141])).
% 2.04/2.27 tff(10163,plain,
% 2.04/2.27 (b(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1786, 10162])).
% 2.04/2.27 tff(10164,plain,
% 2.04/2.27 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(z, s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[9848])).
% 2.04/2.27 tff(10165,plain,
% 2.04/2.27 (~b(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8446, 10164])).
% 2.04/2.27 tff(10166,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1592, 10165])).
% 2.04/2.27 tff(10167,plain,(b(elem!1, s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(10168,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10167, 10163, 56])).
% 2.04/2.27 tff(10169,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))), s(s(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(X1, 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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10170,plain,
% 2.04/2.27 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10171,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(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(X1, 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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10170])).
% 2.04/2.27 tff(10172,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(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(X1, 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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10171, 10169])).
% 2.04/2.27 tff(10173,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10174,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10173, 10172])).
% 2.04/2.27 tff(10175,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10174, 337, 10101, 1603, 10168, 10153])).
% 2.04/2.27 tff(10176,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10056, 10175, 10161])).
% 2.04/2.27 tff(10177,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10178,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10179,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10178, 10177])).
% 2.04/2.27 tff(10180,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10179, 189, 10176, 10156, 10103])).
% 2.04/2.27 tff(10181,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(10182,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10181, 4946, 2, 56, 1141, 9902, 10092, 791])).
% 2.04/2.27 tff(10183,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[857, 10182, 10097])).
% 2.04/2.27 tff(10184,plain,
% 2.04/2.27 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[9910, 189, 10183, 10095])).
% 2.04/2.27 tff(10185,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2268, 10184])).
% 2.04/2.27 tff(10186,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10187,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10188,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10187, 10186])).
% 2.04/2.27 tff(10189,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10188, 189, 10183, 10095])).
% 2.04/2.27 tff(10190,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[9040, 10189])).
% 2.04/2.27 tff(10191,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10192,plain,
% 2.04/2.27 (((~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(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(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(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10193,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))), s(s(s(s(z))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10192])).
% 2.04/2.27 tff(10194,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10193, 10191])).
% 2.04/2.27 tff(10195,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10196,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[10195, 10194])).
% 2.04/2.27 tff(10197,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[10196, 337, 2, 10185, 10190])).
% 2.04/2.27 tff(10198,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4268, 10197])).
% 2.04/2.27 tff(10199,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10200,plain,
% 2.04/2.27 (((~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)))), s(s(s(z))))) | (~b(s(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(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(10201,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[10200])).
% 2.04/2.27 tff(10202,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[10201, 10199])).
% 2.04/2.27 tff(10203,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(10204,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10203, 10202])).
% 2.04/2.28 tff(10205,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10204, 337, 3243, 2, 1396, 3242])).
% 2.04/2.28 tff(10206,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 10205])).
% 2.04/2.28 tff(10207,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10155, 3250])).
% 2.04/2.28 tff(10208,plain,
% 2.04/2.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(z)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10209,plain,
% 2.04/2.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10210,plain,
% 2.04/2.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10209, 10208])).
% 2.04/2.28 tff(10211,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10210, 189, 3301, 10207, 10206])).
% 2.04/2.28 tff(10212,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), 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(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10213,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10212, 10198, 4946, 2, 10185])).
% 2.04/2.28 tff(10214,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10027, 10213])).
% 2.04/2.28 tff(10215,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10127, 189, 1141, 10214])).
% 2.04/2.28 tff(10216,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 10215])).
% 2.04/2.28 tff(10217,plain,
% 2.04/2.28 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[56])).
% 2.04/2.28 tff(10218,plain,
% 2.04/2.28 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[10217])).
% 2.04/2.28 tff(10219,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10220,plain,
% 2.04/2.28 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10221,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~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(X1, 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(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10220])).
% 2.04/2.28 tff(10222,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~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(X1, 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(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10221, 10219])).
% 2.04/2.28 tff(10223,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10224,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10223, 10222])).
% 2.04/2.28 tff(10225,plain,
% 2.04/2.28 (~b(elem!1, s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10224, 337, 10093, 791, 9902])).
% 2.04/2.28 tff(10226,plain,
% 2.04/2.28 (r(elem!1, s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9064, 10225, 9863])).
% 2.04/2.28 tff(10227,plain,
% 2.04/2.28 (r(z, s(s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10226, 10218])).
% 2.04/2.28 tff(10228,plain,
% 2.04/2.28 (~b(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4311, 337, 3243, 2, 1592])).
% 2.04/2.28 tff(10229,plain,
% 2.04/2.28 (r(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1312, 43, 178, 10228])).
% 2.04/2.28 tff(10230,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10231,plain,
% 2.04/2.28 (((~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)))), 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(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)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10232,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(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(X1, 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))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10231])).
% 2.04/2.28 tff(10233,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(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(X1, 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)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10232, 10230])).
% 2.04/2.28 tff(10234,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10235,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10234, 10233])).
% 2.04/2.28 tff(10236,plain,
% 2.04/2.28 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10235, 337, 3243, 2, 1396])).
% 2.04/2.28 tff(10237,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1360, 43, 458, 10236])).
% 2.04/2.28 tff(10238,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6733, 189, 1116, 10237, 10229])).
% 2.04/2.28 tff(10239,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(s(s(z))) = s(s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10240,plain,
% 2.04/2.28 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10239, 2009])).
% 2.04/2.28 tff(10241,plain,
% 2.04/2.28 (~b(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10240, 10185, 2, 4946, 10227])).
% 2.04/2.28 tff(10242,plain,
% 2.04/2.28 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9851, 10241, 56])).
% 2.04/2.28 tff(10243,plain,
% 2.04/2.28 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2845, 43, 9858, 10242])).
% 2.04/2.28 tff(10244,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10051, 189, 10243, 10214])).
% 2.04/2.28 tff(10245,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10056, 10244, 10161])).
% 2.04/2.28 tff(10246,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), 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(X1, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10247,plain,
% 2.04/2.28 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10248,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10247])).
% 2.04/2.28 tff(10249,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), 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(X1, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10248, 10246])).
% 2.04/2.28 tff(10250,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10251,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10250, 10249])).
% 2.04/2.28 tff(10252,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10251, 337, 10093, 791, 10245, 10216])).
% 2.04/2.28 tff(10253,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10254,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10253, 9806, 10089, 2, 9800, 49])).
% 2.04/2.28 tff(10255,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[851, 10254])).
% 2.04/2.28 tff(10256,plain,
% 2.04/2.28 (elem!1 = z),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4411, 9800])).
% 2.04/2.28 tff(10257,plain,
% 2.04/2.28 (~r(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9884, 9806, 49, 9800])).
% 2.04/2.28 tff(10258,plain,
% 2.04/2.28 (b(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[80, 10257])).
% 2.04/2.28 tff(10259,plain,
% 2.04/2.28 (b(elem!1, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4863, 10258, 10256])).
% 2.04/2.28 tff(10260,plain,
% 2.04/2.28 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9800])).
% 2.04/2.28 tff(10261,plain,
% 2.04/2.28 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10260, 2114])).
% 2.04/2.28 tff(10262,plain,
% 2.04/2.28 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.28 inference(transitivity,[status(thm)],[10261, 2115])).
% 2.04/2.28 tff(10263,plain,
% 2.04/2.28 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10262])).
% 2.04/2.28 tff(10264,plain,
% 2.04/2.28 (~(s(s(z)) = elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[31, 10263])).
% 2.04/2.28 tff(10265,plain,
% 2.04/2.28 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9800])).
% 2.04/2.28 tff(10266,plain,
% 2.04/2.28 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10265])).
% 2.04/2.28 tff(10267,plain,
% 2.04/2.28 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[817, 10266])).
% 2.04/2.28 tff(10268,plain,
% 2.04/2.28 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9602, 337, 10259, 9806, 10255])).
% 2.04/2.28 tff(10269,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[857, 10268, 10267])).
% 2.04/2.28 tff(10270,plain,
% 2.04/2.28 (~b(s(s(z)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9928, 10269, 10264, 10259, 9806, 10255])).
% 2.04/2.28 tff(10271,plain,
% 2.04/2.28 (r(s(s(z)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2229, 10270])).
% 2.04/2.28 tff(10272,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1293, 189, 49, 10271])).
% 2.04/2.28 tff(10273,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4268, 10272])).
% 2.04/2.28 tff(10274,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7348, 189, 49, 10271])).
% 2.04/2.28 tff(10275,plain,
% 2.04/2.28 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2854, 10274])).
% 2.04/2.28 tff(10276,plain,
% 2.04/2.28 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8224, 337, 10259, 9806, 10255])).
% 2.04/2.28 tff(10277,plain,
% 2.04/2.28 (~b(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10167, 10276, 9800])).
% 2.04/2.28 tff(10278,plain,
% 2.04/2.28 (r(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1786, 10277])).
% 2.04/2.28 tff(10279,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4348, 10278, 10258, 9806, 10259, 10089])).
% 2.04/2.28 tff(10280,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2268, 10279])).
% 2.04/2.28 tff(10281,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~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(z))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10282,plain,
% 2.04/2.28 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), 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(z), elem!1)) | (~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(z))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10283,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(z))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10282])).
% 2.04/2.28 tff(10284,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~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(z))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10283, 10281])).
% 2.04/2.28 tff(10285,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), 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)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10286,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10285, 10284])).
% 2.04/2.28 tff(10287,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10286, 337, 791, 2, 1231, 1396, 2856, 9658])).
% 2.04/2.28 tff(10288,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(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(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10289,plain,
% 2.04/2.28 (~b(s(s(z)), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10288, 9806, 2, 10255, 10280, 10275])).
% 2.04/2.28 tff(10290,plain,
% 2.04/2.28 (r(s(s(z)), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2301, 10289, 10264])).
% 2.04/2.28 tff(10291,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10188, 189, 10269, 10290])).
% 2.04/2.28 tff(10292,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9040, 10291])).
% 2.04/2.28 tff(10293,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10196, 337, 2, 10280, 10292, 10273])).
% 2.04/2.28 tff(10294,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10295,plain,
% 2.04/2.28 (b(s(s(s(z))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10294, 2, 1])).
% 2.04/2.28 tff(10296,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1198, 189, 811, 4222, 2245])).
% 2.04/2.28 tff(10297,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(10298,plain,
% 2.04/2.28 (~r(s(s(z)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10297, 811, 4222])).
% 2.04/2.28 tff(10299,plain,
% 2.04/2.28 (b(s(s(z)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2229, 10298])).
% 2.04/2.28 tff(10300,plain,
% 2.04/2.28 (~b(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6693, 337, 1, 1301, 3357])).
% 2.04/2.28 tff(10301,plain,
% 2.04/2.28 (r(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2242, 10300])).
% 2.04/2.28 tff(10302,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10303,plain,
% 2.04/2.28 (((~b(z, s(z))) | (~b(s(s(z)), 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(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(10304,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), 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(X1, 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))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[10303])).
% 2.04/2.28 tff(10305,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), 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(X1, 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))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[10304, 10302])).
% 2.04/2.28 tff(10306,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), 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)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(10307,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[10306, 10305])).
% 2.04/2.28 tff(10308,plain,
% 2.04/2.28 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[10307, 337, 1, 1301, 1658, 3357])).
% 2.04/2.28 tff(10309,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2854, 10308])).
% 2.04/2.28 tff(10310,plain,
% 2.04/2.28 (~b(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4299, 1301, 1, 1658])).
% 2.04/2.29 tff(10311,plain,
% 2.04/2.29 (r(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1498, 10310])).
% 2.04/2.29 tff(10312,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8845, 189, 10311, 10309, 10301])).
% 2.04/2.29 tff(10313,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10314,plain,
% 2.04/2.29 (~b(z, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10313, 10299, 10295, 1])).
% 2.04/2.29 tff(10315,plain,
% 2.04/2.29 (r(z, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[80, 10314])).
% 2.04/2.29 tff(10316,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10317,plain,
% 2.04/2.29 (((~b(z, s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10318,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10317])).
% 2.04/2.29 tff(10319,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10318, 10316])).
% 2.04/2.29 tff(10320,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10321,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10320, 10319])).
% 2.04/2.29 tff(10322,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10321, 337, 1, 1275, 8178, 2400])).
% 2.04/2.29 tff(10323,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10324,plain,
% 2.04/2.29 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10323, 10315, 1, 811])).
% 2.04/2.29 tff(10325,plain,
% 2.04/2.29 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1150, 10324])).
% 2.04/2.29 tff(10326,plain,
% 2.04/2.29 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10151, 10325, 4222, 10299])).
% 2.04/2.29 tff(10327,plain,
% 2.04/2.29 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10027, 10326])).
% 2.04/2.29 tff(10328,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2023, 10315, 811])).
% 2.04/2.29 tff(10329,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1792, 10328])).
% 2.04/2.29 tff(10330,plain,
% 2.04/2.29 (~r(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8078, 10315, 811])).
% 2.04/2.29 tff(10331,plain,
% 2.04/2.29 (b(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1786, 10330])).
% 2.04/2.29 tff(10332,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))), 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(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10333,plain,
% 2.04/2.29 (((~b(z, s(s(s(s(z)))))) | (~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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10334,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10333])).
% 2.04/2.29 tff(10335,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10334, 10332])).
% 2.04/2.29 tff(10336,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(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))))), z)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10337,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10336, 10335])).
% 2.04/2.29 tff(10338,plain,
% 2.04/2.29 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10337, 337, 10331, 10329, 10327])).
% 2.04/2.29 tff(10339,plain,
% 2.04/2.29 (((~![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))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10340,plain,
% 2.04/2.29 ((~![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))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10341,plain,
% 2.04/2.29 ((~![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)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10340, 10339])).
% 2.04/2.29 tff(10342,plain,
% 2.04/2.29 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 10338])).
% 2.04/2.29 tff(10343,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), 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(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10344,plain,
% 2.04/2.29 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(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(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10345,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10344])).
% 2.04/2.29 tff(10346,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10345, 10343])).
% 2.04/2.29 tff(10347,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(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(s(s(s(z))))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10348,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10347, 10346])).
% 2.04/2.29 tff(10349,plain,
% 2.04/2.29 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10348, 337, 2, 10331, 10329, 10327])).
% 2.04/2.29 tff(10350,plain,
% 2.04/2.29 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6662])).
% 2.04/2.29 tff(10351,plain,
% 2.04/2.29 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10010, 10350])).
% 2.04/2.29 tff(10352,plain,
% 2.04/2.29 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2489, 10351])).
% 2.04/2.29 tff(10353,plain,
% 2.04/2.29 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10352, 10349])).
% 2.04/2.29 tff(10354,plain,
% 2.04/2.29 (~b(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8180, 10315, 2, 811])).
% 2.04/2.29 tff(10355,plain,
% 2.04/2.29 (r(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1498, 10354])).
% 2.04/2.29 tff(10356,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10357,plain,
% 2.04/2.29 (((~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(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10358,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10357])).
% 2.04/2.29 tff(10359,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10358, 10356])).
% 2.04/2.29 tff(10360,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10361,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10360, 10359])).
% 2.04/2.29 tff(10362,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10361, 189, 10355, 10353, 10342])).
% 2.04/2.29 tff(10363,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10364,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10363, 4222, 2, 1])).
% 2.04/2.29 tff(10365,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[851, 10364])).
% 2.04/2.29 tff(10366,plain,
% 2.04/2.29 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4840, 337, 1, 2, 10365, 10295])).
% 2.04/2.29 tff(10367,plain,
% 2.04/2.29 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1150, 10366])).
% 2.04/2.29 tff(10368,plain,
% 2.04/2.29 (~r(s(s(z)), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4227, 189, 10367, 4222])).
% 2.04/2.29 tff(10369,plain,
% 2.04/2.29 (b(s(s(z)), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2229, 10368])).
% 2.04/2.29 tff(10370,plain,
% 2.04/2.29 (~r(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10137, 10367, 4222])).
% 2.04/2.29 tff(10371,plain,
% 2.04/2.29 (b(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8207, 10370])).
% 2.04/2.29 tff(10372,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10373,plain,
% 2.04/2.29 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(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)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10374,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10373])).
% 2.04/2.29 tff(10375,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10374, 10372])).
% 2.04/2.29 tff(10376,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(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)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10377,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10376, 10375])).
% 2.04/2.29 tff(10378,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10377, 337, 2, 10365, 10371, 10295, 10369])).
% 2.04/2.29 tff(10379,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10380,plain,
% 2.04/2.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10379, 2, 1])).
% 2.04/2.29 tff(10381,plain,
% 2.04/2.29 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2268, 10380])).
% 2.04/2.29 tff(10382,assumption,(z = s(s(z))), introduced(assumption)).
% 2.04/2.29 tff(10383,plain,
% 2.04/2.29 (s(s(z)) = z),
% 2.04/2.29 inference(symmetry,[status(thm)],[10382])).
% 2.04/2.29 tff(10384,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[31, 10383])).
% 2.04/2.29 tff(10385,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10386,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(s(s(s(z)))))) | (~b(s(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(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10387,plain,
% 2.04/2.29 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10388,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10387])).
% 2.04/2.29 tff(10389,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10388, 10386])).
% 2.04/2.29 tff(10390,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10391,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10390, 10389])).
% 2.04/2.29 tff(10392,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10391, 337, 1, 1301, 2, 1231, 10295])).
% 2.04/2.29 tff(10393,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(10394,plain,
% 2.04/2.29 (~b(z, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[10393, 1231, 2, 1])).
% 2.04/2.29 tff(10395,plain,
% 2.04/2.29 (r(z, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[80, 10394])).
% 2.04/2.29 tff(10396,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10397,plain,
% 2.04/2.29 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(10398,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[10397])).
% 2.04/2.29 tff(10399,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[10398, 10396])).
% 2.04/2.29 tff(10400,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(10401,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[10400, 10399])).
% 2.04/2.29 tff(10402,plain,
% 2.04/2.29 (~r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10401, 189, 10395, 2245])).
% 2.14/2.30 tff(10403,plain,
% 2.14/2.30 (b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9005, 43, 10402, 10385])).
% 2.14/2.30 tff(10404,plain,
% 2.14/2.30 (~r(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2253, 10395, 2245])).
% 2.14/2.30 tff(10405,plain,
% 2.14/2.30 (b(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2242, 10404])).
% 2.14/2.30 tff(10406,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10407,plain,
% 2.14/2.30 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10408,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10407])).
% 2.14/2.30 tff(10409,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[10408, 10406])).
% 2.14/2.30 tff(10410,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10411,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10410, 10409])).
% 2.14/2.30 tff(10412,plain,
% 2.14/2.30 (~b(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10411, 337, 1, 10381, 10405, 10403])).
% 2.14/2.30 tff(10413,plain,
% 2.14/2.30 (r(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8207, 10412])).
% 2.14/2.30 tff(10414,plain,
% 2.14/2.30 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4840, 337, 1, 2, 1231, 10295])).
% 2.14/2.30 tff(10415,plain,
% 2.14/2.30 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1150, 10414])).
% 2.14/2.30 tff(10416,plain,
% 2.14/2.30 (~r(z, s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1580, 10395, 10415])).
% 2.14/2.30 tff(10417,plain,
% 2.14/2.30 (b(z, s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1786, 10416])).
% 2.14/2.30 tff(10418,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10419,plain,
% 2.14/2.30 (((~b(s(s(s(s(z)))), 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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(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))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10420,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(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)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10419])).
% 2.14/2.30 tff(10421,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[10420, 10418])).
% 2.14/2.30 tff(10422,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10423,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10422, 10421])).
% 2.14/2.30 tff(10424,plain,
% 2.14/2.30 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10423, 337, 1231, 10381, 10417, 10403])).
% 2.14/2.30 tff(10425,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9040, 10424])).
% 2.14/2.30 tff(10426,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10427,plain,
% 2.14/2.30 (((~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(s(s(z)))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10428,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))), s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10427])).
% 2.14/2.30 tff(10429,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))), s(s(z)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[10428, 10426])).
% 2.14/2.30 tff(10430,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10431,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10430, 10429])).
% 2.14/2.30 tff(10432,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10431, 189, 10415, 10425, 10413])).
% 2.14/2.30 tff(10433,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(10434,plain,
% 2.14/2.30 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10433, 2245, 1, 2])).
% 2.14/2.30 tff(10435,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[851, 10434])).
% 2.14/2.30 tff(10436,plain,
% 2.14/2.30 (~r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10401, 189, 173, 2245])).
% 2.14/2.30 tff(10437,plain,
% 2.14/2.30 (b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9005, 43, 10436, 10385])).
% 2.14/2.30 tff(10438,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10439,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10440,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10439, 10438])).
% 2.14/2.30 tff(10441,plain,
% 2.14/2.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10440, 189, 811, 2245])).
% 2.14/2.30 tff(10442,plain,
% 2.14/2.30 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9040, 10441])).
% 2.14/2.30 tff(10443,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1209, 337, 1396, 10442, 2400, 10437])).
% 2.14/2.30 tff(10444,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(10445,plain,
% 2.14/2.30 (~r(z, s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10444, 10435, 10381, 2245])).
% 2.14/2.30 tff(10446,plain,
% 2.14/2.30 (b(z, s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[80, 10445])).
% 2.14/2.30 tff(10447,plain,
% 2.14/2.30 (~b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4299, 10446, 1, 10295])).
% 2.14/2.30 tff(10448,plain,
% 2.14/2.30 (r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1498, 10447])).
% 2.14/2.30 tff(10449,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10450,plain,
% 2.14/2.30 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10451,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10450])).
% 2.14/2.30 tff(10452,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[10451, 10449])).
% 2.14/2.30 tff(10453,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10454,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10453, 10452])).
% 2.14/2.30 tff(10455,plain,
% 2.14/2.30 (~b(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10454, 337, 1, 10446, 10295])).
% 2.14/2.30 tff(10456,plain,
% 2.14/2.30 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[199, 43, 10455])).
% 2.14/2.30 tff(10457,plain,
% 2.14/2.30 (r(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10456, 179])).
% 2.14/2.30 tff(10458,plain,
% 2.14/2.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10440, 189, 10435, 2245])).
% 2.14/2.30 tff(10459,plain,
% 2.14/2.30 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9040, 10458])).
% 2.14/2.30 tff(10460,plain,
% 2.14/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10196, 337, 2, 10381, 10459])).
% 2.14/2.30 tff(10461,plain,
% 2.14/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4268, 10460])).
% 2.14/2.30 tff(10462,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10463,plain,
% 2.14/2.30 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10464,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10463])).
% 2.14/2.30 tff(10465,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[10464, 10462])).
% 2.14/2.30 tff(10466,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(10467,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[10466, 10465])).
% 2.14/2.30 tff(10468,plain,
% 2.14/2.30 (~r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10467, 189, 10461, 10457])).
% 2.14/2.30 tff(10469,plain,
% 2.14/2.30 (b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9005, 43, 10468, 10385])).
% 2.14/2.30 tff(10470,plain,
% 2.14/2.30 (~b(s(s(s(s(z)))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1209, 337, 10381, 10459, 10469])).
% 2.14/2.30 tff(10471,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1792, 10470])).
% 2.14/2.30 tff(10472,plain,
% 2.14/2.30 ((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[7566, 10026, 10010])).
% 2.14/2.30 tff(10473,plain,
% 2.14/2.30 (~r(s(s(s(s(s(z))))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10472, 10471, 2, 10448])).
% 2.14/2.30 tff(10474,plain,
% 2.14/2.30 (b(s(s(s(s(s(z))))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 10473])).
% 2.14/2.30 tff(10475,plain,
% 2.14/2.30 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[7557, 189, 10448, 10471])).
% 2.14/2.30 tff(10476,plain,
% 2.14/2.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[524, 10475])).
% 2.14/2.30 tff(10477,plain,
% 2.14/2.30 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10212, 10476, 10381, 2, 10461])).
% 2.14/2.30 tff(10478,plain,
% 2.14/2.30 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[10027, 10477])).
% 2.14/2.30 tff(10479,plain,
% 2.14/2.30 (~r(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4275, 189, 10461, 10457])).
% 2.14/2.30 tff(10480,plain,
% 2.14/2.30 (b(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2242, 10479])).
% 2.14/2.30 tff(10481,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10482,plain,
% 2.14/2.30 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(10483,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[10482])).
% 2.14/2.30 tff(10484,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10483, 10481])).
% 2.14/2.31 tff(10485,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10486,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10485, 10484])).
% 2.14/2.31 tff(10487,plain,
% 2.14/2.31 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10486, 337, 1, 2, 10459, 10480, 10295])).
% 2.14/2.31 tff(10488,plain,
% 2.14/2.31 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1150, 10487])).
% 2.14/2.31 tff(10489,plain,
% 2.14/2.31 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10127, 189, 10488, 10478])).
% 2.14/2.31 tff(10490,plain,
% 2.14/2.31 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 10489])).
% 2.14/2.31 tff(10491,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10492,plain,
% 2.14/2.31 (((~b(z, s(z))) | (~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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10493,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10492])).
% 2.14/2.31 tff(10494,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X1, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10493, 10491])).
% 2.14/2.31 tff(10495,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10496,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10495, 10494])).
% 2.14/2.31 tff(10497,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10496, 337, 1, 10446, 10490, 10474])).
% 2.14/2.31 tff(10498,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(10499,plain,
% 2.14/2.31 (~r(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10498, 2, 1])).
% 2.14/2.31 tff(10500,plain,
% 2.14/2.31 (b(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2229, 10499])).
% 2.14/2.31 tff(10501,plain,
% 2.14/2.31 (~b(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10313, 10500, 10295, 1])).
% 2.14/2.31 tff(10502,plain,
% 2.14/2.31 (r(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[80, 10501])).
% 2.14/2.31 tff(10503,plain,
% 2.14/2.31 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3056, 337, 1275, 1231, 3357])).
% 2.14/2.31 tff(10504,plain,
% 2.14/2.31 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2268, 10503])).
% 2.14/2.31 tff(10505,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(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(X1, 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(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10506,plain,
% 2.14/2.31 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10507,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(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(X1, 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(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10506])).
% 2.14/2.31 tff(10508,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(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(X1, 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(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10507, 10505])).
% 2.14/2.31 tff(10509,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(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))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10510,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10509, 10508])).
% 2.14/2.31 tff(10511,plain,
% 2.14/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10510, 337, 1275, 1231, 1658, 3357])).
% 2.14/2.31 tff(10512,plain,
% 2.14/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4267, 10511, 2008])).
% 2.14/2.31 tff(10513,plain,
% 2.14/2.31 (((~b(s(s(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(z))) | (~b(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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10514,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10513])).
% 2.14/2.31 tff(10515,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10514, 1276])).
% 2.14/2.31 tff(10516,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10517,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10516, 10515])).
% 2.14/2.31 tff(10518,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10517, 337, 1275, 1231, 1658])).
% 2.14/2.31 tff(10519,plain,
% 2.14/2.31 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[548, 10518])).
% 2.14/2.31 tff(10520,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3590, 189, 10519, 10512, 10504])).
% 2.14/2.31 tff(10521,plain,((~b(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)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(10522,plain,
% 2.14/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10521, 1275, 1658, 3357])).
% 2.14/2.31 tff(10523,plain,
% 2.14/2.31 (~b(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10313, 3357, 1658, 1])).
% 2.14/2.31 tff(10524,plain,
% 2.14/2.31 (r(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[80, 10523])).
% 2.14/2.31 tff(10525,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10323, 1275, 1, 10524])).
% 2.14/2.31 tff(10526,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[851, 10525, 10522])).
% 2.14/2.31 tff(10527,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(10528,plain,
% 2.14/2.31 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10527, 10295, 1, 10500])).
% 2.14/2.31 tff(10529,plain,
% 2.14/2.31 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1150, 10528])).
% 2.14/2.31 tff(10530,plain,
% 2.14/2.31 (~r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1580, 10529, 10502])).
% 2.14/2.31 tff(10531,plain,
% 2.14/2.31 (b(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1786, 10530])).
% 2.14/2.31 tff(10532,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10533,plain,
% 2.14/2.31 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(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(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10534,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10533])).
% 2.14/2.31 tff(10535,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10534, 10532])).
% 2.14/2.31 tff(10536,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10537,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10536, 10535])).
% 2.14/2.31 tff(10538,plain,
% 2.14/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10537, 337, 1, 2, 10531, 10295, 10500])).
% 2.14/2.31 tff(10539,plain,
% 2.14/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4268, 10538])).
% 2.14/2.31 tff(10540,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))), z)))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10541,plain,
% 2.14/2.31 (((~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)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(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)))), z)))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10542,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), 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(X1, 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(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)))), z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10541])).
% 2.14/2.31 tff(10543,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), 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(X1, 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(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)))), z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[10542, 10540])).
% 2.14/2.31 tff(10544,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(10545,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))), z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[10544, 10543])).
% 2.14/2.31 tff(10546,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[10545, 337, 2, 1396, 1592, 2400])).
% 2.14/2.31 tff(10547,plain,
% 2.14/2.31 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2854, 10546])).
% 2.14/2.31 tff(10548,plain,
% 2.14/2.31 (~b(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8180, 811, 2, 173])).
% 2.14/2.31 tff(10549,plain,
% 2.14/2.31 (r(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1498, 10548])).
% 2.14/2.31 tff(10550,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10551,plain,
% 2.14/2.31 (((~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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(10552,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[10551])).
% 2.14/2.32 tff(10553,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10552, 10550])).
% 2.14/2.32 tff(10554,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10555,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10554, 10553])).
% 2.14/2.32 tff(10556,plain,
% 2.14/2.32 (~b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10555, 337, 1396, 1592, 2400])).
% 2.14/2.32 tff(10557,plain,
% 2.14/2.32 (r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9005, 43, 10556, 10385])).
% 2.14/2.32 tff(10558,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6733, 189, 10557, 10549, 10547])).
% 2.14/2.32 tff(10559,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(10560,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10559, 10381, 10531, 2, 10502])).
% 2.14/2.32 tff(10561,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[851, 10560])).
% 2.14/2.32 tff(10562,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10563,plain,
% 2.14/2.32 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), 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(z), z)) | (~b(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(s(s(z)))), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10564,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), 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(X1, 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(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(z)))), s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10563])).
% 2.14/2.32 tff(10565,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), 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(X1, 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(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(z)))), s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10564, 10562])).
% 2.14/2.32 tff(10566,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10567,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 2.14/2.32 tff(10568,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10567, 337, 1, 10561, 10381, 10531, 10500])).
% 2.14/2.32 tff(10569,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9040, 10568])).
% 2.14/2.32 tff(10570,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10571,plain,
% 2.14/2.32 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(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(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(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10572,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10571])).
% 2.14/2.32 tff(10573,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10572, 10570])).
% 2.14/2.32 tff(10574,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10575,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10574, 10573])).
% 2.14/2.32 tff(10576,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10575, 337, 1, 2, 10561, 10531, 10295])).
% 2.14/2.32 tff(10577,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[524, 10576])).
% 2.14/2.32 tff(10578,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10579,plain,
% 2.14/2.32 (((~r(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(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10580,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10579])).
% 2.14/2.32 tff(10581,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10580, 10578])).
% 2.14/2.32 tff(10582,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10583,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10582, 10581])).
% 2.14/2.32 tff(10584,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10583, 189, 10577, 10569, 10539])).
% 2.14/2.32 tff(10585,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(10586,plain,
% 2.14/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10585, 1])).
% 2.14/2.32 tff(10587,plain,
% 2.14/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[548, 10586])).
% 2.14/2.32 tff(10588,plain,
% 2.14/2.32 (s(s(elem!1)) = s(s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9799])).
% 2.14/2.32 tff(10589,plain,
% 2.14/2.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10588])).
% 2.14/2.32 tff(10590,plain,
% 2.14/2.32 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10589])).
% 2.14/2.32 tff(10591,plain,
% 2.14/2.32 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10590])).
% 2.14/2.32 tff(10592,plain,
% 2.14/2.32 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9800])).
% 2.14/2.32 tff(10593,plain,
% 2.14/2.32 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10592, 3256])).
% 2.14/2.32 tff(10594,plain,
% 2.14/2.32 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10593])).
% 2.14/2.32 tff(10595,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[659, 10594])).
% 2.14/2.32 tff(10596,plain,
% 2.14/2.32 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10590, 9799])).
% 2.14/2.32 tff(10597,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[10596])).
% 2.14/2.32 tff(10598,plain,
% 2.14/2.32 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[1231, 10597])).
% 2.14/2.32 tff(10599,plain,
% 2.14/2.32 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9799])).
% 2.14/2.32 tff(10600,plain,
% 2.14/2.32 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[10599])).
% 2.14/2.32 tff(10601,plain,
% 2.14/2.32 (b(elem!1, s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10259, 10600])).
% 2.14/2.32 tff(10602,plain,
% 2.14/2.32 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3580, 10601, 9805, 10598])).
% 2.14/2.32 tff(10603,plain,
% 2.14/2.32 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3274, 10602, 10595])).
% 2.14/2.32 tff(10604,plain,
% 2.14/2.32 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10603, 10591])).
% 2.14/2.32 tff(10605,plain,
% 2.14/2.32 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9800])).
% 2.14/2.32 tff(10606,plain,
% 2.14/2.32 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10605, 10040])).
% 2.14/2.32 tff(10607,plain,
% 2.14/2.32 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.14/2.32 inference(transitivity,[status(thm)],[10606, 10041])).
% 2.14/2.32 tff(10608,plain,
% 2.14/2.32 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10607])).
% 2.14/2.32 tff(10609,plain,
% 2.14/2.32 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10047, 10608])).
% 2.14/2.32 tff(10610,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10611,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10612,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10611, 10610])).
% 2.14/2.32 tff(10613,plain,
% 2.14/2.32 (~r(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10612, 189, 10587, 10604])).
% 2.14/2.32 tff(10614,plain,
% 2.14/2.32 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9800])).
% 2.14/2.32 tff(10615,plain,
% 2.14/2.32 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10614, 5931])).
% 2.14/2.32 tff(10616,plain,
% 2.14/2.32 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10615])).
% 2.14/2.32 tff(10617,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[178, 10616])).
% 2.14/2.32 tff(10618,plain,
% 2.14/2.32 (b(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5966, 43, 10617, 10613])).
% 2.14/2.32 tff(10619,plain,
% 2.14/2.32 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2027, 49, 10587])).
% 2.14/2.32 tff(10620,plain,
% 2.14/2.32 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1150, 10619])).
% 2.14/2.32 tff(10621,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9889, 10259, 10620, 9806])).
% 2.14/2.32 tff(10622,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[857, 10621, 10267])).
% 2.14/2.32 tff(10623,plain,
% 2.14/2.32 (~b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9928, 10622, 10264, 10259, 9806, 1231])).
% 2.14/2.32 tff(10624,plain,
% 2.14/2.32 (r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2229, 10623])).
% 2.14/2.32 tff(10625,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1293, 189, 49, 10624])).
% 2.14/2.32 tff(10626,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4268, 10625])).
% 2.14/2.32 tff(10627,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[7348, 189, 49, 10624])).
% 2.14/2.32 tff(10628,plain,
% 2.14/2.32 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2854, 10627])).
% 2.14/2.32 tff(10629,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.14/2.32 tff(10630,plain,
% 2.14/2.32 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10155, 7912])).
% 2.14/2.32 tff(10631,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 2.14/2.32 tff(10632,plain,
% 2.14/2.32 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10051, 189, 4156, 7908])).
% 2.14/2.32 tff(10633,plain,
% 2.14/2.32 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10056, 10632, 10631])).
% 2.14/2.32 tff(10634,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10635,plain,
% 2.14/2.32 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10636,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10635])).
% 2.14/2.32 tff(10637,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(X1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10636, 10634])).
% 2.14/2.32 tff(10638,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10639,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10638, 10637])).
% 2.14/2.32 tff(10640,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10639, 337, 2856, 10633, 7403, 10630, 10629])).
% 2.14/2.32 tff(10641,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(10642,plain,
% 2.14/2.32 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10641, 10628, 10626, 10618, 10609, 10604, 10587])).
% 2.14/2.32 tff(10643,plain,
% 2.14/2.32 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10027, 10642])).
% 2.14/2.32 tff(10644,plain,
% 2.14/2.32 (~b(s(z), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3268, 337, 10620, 1231, 10643])).
% 2.14/2.32 tff(10645,plain,
% 2.14/2.32 (r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[7948, 10644])).
% 2.14/2.32 tff(10646,plain,
% 2.14/2.32 (~b(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8224, 337, 10259, 9806, 1231])).
% 2.14/2.32 tff(10647,plain,
% 2.14/2.32 (~b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[10167, 10646, 9800])).
% 2.14/2.32 tff(10648,plain,
% 2.14/2.32 (r(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1786, 10647])).
% 2.14/2.32 tff(10649,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5133, 10648, 10587, 10258])).
% 2.14/2.32 tff(10650,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2268, 10649])).
% 2.14/2.32 tff(10651,plain,
% 2.14/2.32 (~b(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1239, 337, 10620, 1231, 10650])).
% 2.14/2.32 tff(10652,plain,
% 2.14/2.32 (r(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8207, 10651])).
% 2.14/2.32 tff(10653,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10654,plain,
% 2.14/2.32 (((~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(z)))), 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(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(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(10655,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[10654])).
% 2.14/2.32 tff(10656,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[10655, 10653])).
% 2.14/2.32 tff(10657,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10658,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10657, 10656])).
% 2.14/2.33 tff(10659,plain,
% 2.14/2.33 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10658, 337, 10620, 1231, 10650, 10643])).
% 2.14/2.33 tff(10660,plain,
% 2.14/2.33 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10142, 10659])).
% 2.14/2.33 tff(10661,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10662,plain,
% 2.14/2.33 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10663,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10662])).
% 2.14/2.33 tff(10664,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10663, 10661])).
% 2.14/2.33 tff(10665,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10666,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10665, 10664])).
% 2.14/2.33 tff(10667,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10666, 189, 10660, 10652, 10645])).
% 2.14/2.33 tff(10668,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10669,plain,
% 2.14/2.33 (b(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10668, 1231, 1])).
% 2.14/2.33 tff(10670,plain,
% 2.14/2.33 (~r(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5118, 189, 10587, 1115])).
% 2.14/2.33 tff(10671,plain,
% 2.14/2.33 (~r(s(s(s(z))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5075, 1115, 10587])).
% 2.14/2.33 tff(10672,plain,
% 2.14/2.33 (b(s(s(s(z))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1498, 10671])).
% 2.14/2.33 tff(10673,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10674,plain,
% 2.14/2.33 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10675,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10674])).
% 2.14/2.33 tff(10676,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10675, 10673])).
% 2.14/2.33 tff(10677,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10678,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10677, 10676])).
% 2.14/2.33 tff(10679,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10678, 337, 1, 1659, 1658, 7771])).
% 2.14/2.33 tff(10680,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10681,plain,
% 2.14/2.33 (~b(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10680, 10672, 1, 1658])).
% 2.14/2.33 tff(10682,plain,
% 2.14/2.33 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[199, 43, 10681])).
% 2.14/2.33 tff(10683,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10682, 10670, 179])).
% 2.14/2.33 tff(10684,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10685,plain,
% 2.14/2.33 (~r(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10684, 10669, 1])).
% 2.14/2.33 tff(10686,plain,
% 2.14/2.33 (b(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1786, 10685])).
% 2.14/2.33 tff(10687,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 2.14/2.33 tff(10688,plain,
% 2.14/2.33 (s(s(s(z))) = s(z)),
% 2.14/2.33 inference(symmetry,[status(thm)],[10687])).
% 2.14/2.33 tff(10689,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[33, 10688])).
% 2.14/2.33 tff(10690,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10691,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 2.14/2.33 tff(10692,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10693,plain,
% 2.14/2.33 (((~b(s(s(s(z))), s(z))) | (~b(s(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(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10694,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10693])).
% 2.14/2.33 tff(10695,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10694, 10692])).
% 2.14/2.33 tff(10696,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10697,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10696, 10695])).
% 2.14/2.33 tff(10698,plain,
% 2.14/2.33 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10697, 337, 1231, 1658, 3357, 10691])).
% 2.14/2.33 tff(10699,plain,
% 2.14/2.33 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2268, 10698])).
% 2.14/2.33 tff(10700,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10701,plain,
% 2.14/2.33 (((~b(s(s(s(z))), s(z))) | (~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(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10702,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10701])).
% 2.14/2.33 tff(10703,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10702, 10700])).
% 2.14/2.33 tff(10704,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10705,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10704, 10703])).
% 2.14/2.33 tff(10706,plain,
% 2.14/2.33 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10705, 337, 1658, 3357, 10691])).
% 2.14/2.33 tff(10707,plain,
% 2.14/2.33 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4268, 10706])).
% 2.14/2.33 tff(10708,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3590, 189, 1339, 3301, 4222])).
% 2.14/2.33 tff(10709,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10710,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10709, 10707, 10699, 1339])).
% 2.14/2.33 tff(10711,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10712,plain,
% 2.14/2.33 (~b(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10711, 3357, 10587, 10669, 1231])).
% 2.14/2.33 tff(10713,plain,
% 2.14/2.33 (r(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2796, 43, 10712, 10690])).
% 2.14/2.33 tff(10714,plain,
% 2.14/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10527, 3357, 1, 10669])).
% 2.14/2.33 tff(10715,plain,
% 2.14/2.33 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1150, 10714])).
% 2.14/2.33 tff(10716,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3687, 189, 10715, 10587, 10713])).
% 2.14/2.33 tff(10717,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10718,plain,
% 2.14/2.33 (~b(s(s(z)), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10717, 1231, 1])).
% 2.14/2.33 tff(10719,plain,
% 2.14/2.33 (r(s(s(z)), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2229, 10718])).
% 2.14/2.33 tff(10720,plain,
% 2.14/2.33 (~r(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10401, 189, 173, 10719])).
% 2.14/2.33 tff(10721,plain,
% 2.14/2.33 (b(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9005, 43, 10720, 10385])).
% 2.14/2.33 tff(10722,plain,
% 2.14/2.33 (~r(s(s(z)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2253, 173, 10719])).
% 2.14/2.33 tff(10723,plain,
% 2.14/2.33 (b(s(s(z)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2242, 10722])).
% 2.14/2.33 tff(10724,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10725,plain,
% 2.14/2.33 (((~b(s(z), z)) | (~b(s(s(z)), 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(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10726,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10725])).
% 2.14/2.33 tff(10727,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10726, 10724])).
% 2.14/2.33 tff(10728,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10729,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10728, 10727])).
% 2.14/2.33 tff(10730,plain,
% 2.14/2.33 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10729, 337, 1, 1231, 10686, 10723, 10721])).
% 2.14/2.33 tff(10731,plain,
% 2.14/2.33 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2268, 10730])).
% 2.14/2.33 tff(10732,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10733,plain,
% 2.14/2.33 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10734,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[10733])).
% 2.14/2.33 tff(10735,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[10734, 10732])).
% 2.14/2.33 tff(10736,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(10737,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[10736, 10735])).
% 2.14/2.33 tff(10738,plain,
% 2.14/2.33 (~b(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10737, 337, 1, 10723, 10721])).
% 2.14/2.33 tff(10739,plain,
% 2.14/2.33 (r(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8207, 10738])).
% 2.14/2.33 tff(10740,plain,
% 2.14/2.33 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10137, 10739, 10731])).
% 2.14/2.33 tff(10741,plain,
% 2.14/2.33 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10709, 4222, 10587])).
% 2.14/2.33 tff(10742,plain,
% 2.14/2.33 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4268, 10741])).
% 2.14/2.33 tff(10743,plain,
% 2.14/2.33 (~r(s(s(s(z))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1355, 189, 10587, 4222])).
% 2.14/2.33 tff(10744,plain,
% 2.14/2.33 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2854, 10743])).
% 2.14/2.33 tff(10745,plain,
% 2.14/2.33 (~r(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5133, 1301, 10587, 4222])).
% 2.14/2.33 tff(10746,plain,
% 2.14/2.33 (b(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1786, 10745])).
% 2.14/2.33 tff(10747,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4738, 337, 1, 1301, 1231, 10746])).
% 2.14/2.33 tff(10748,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(10749,plain,
% 2.14/2.33 (~b(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10748, 4222, 1231, 1])).
% 2.14/2.33 tff(10750,plain,
% 2.14/2.33 (r(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[80, 10749])).
% 2.14/2.33 tff(10751,plain,
% 2.14/2.33 (~r(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[10401, 189, 10750, 10719])).
% 2.14/2.33 tff(10752,plain,
% 2.14/2.33 (b(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9005, 43, 10751, 10385])).
% 2.14/2.33 tff(10753,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10754,plain,
% 2.14/2.33 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(10755,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10754])).
% 2.14/2.34 tff(10756,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10755, 10753])).
% 2.14/2.34 tff(10757,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10758,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10757, 10756])).
% 2.14/2.34 tff(10759,plain,
% 2.14/2.34 (~b(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10758, 337, 10752, 10669, 10744, 10742])).
% 2.14/2.34 tff(10760,plain,
% 2.14/2.34 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[199, 43, 10759])).
% 2.14/2.34 tff(10761,plain,
% 2.14/2.34 (r(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10760, 179])).
% 2.14/2.34 tff(10762,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10763,plain,
% 2.14/2.34 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(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(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10764,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10763])).
% 2.14/2.34 tff(10765,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10764, 10762])).
% 2.14/2.34 tff(10766,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10767,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 2.14/2.34 tff(10768,plain,
% 2.14/2.34 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10767, 337, 1275, 1231, 10669])).
% 2.14/2.34 tff(10769,plain,
% 2.14/2.34 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[524, 10768])).
% 2.14/2.34 tff(10770,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7616, 189, 10769, 10761])).
% 2.14/2.34 tff(10771,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1792, 10770])).
% 2.14/2.34 tff(10772,plain,
% 2.14/2.34 (~r(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7507, 10752, 10587, 10742, 10744])).
% 2.14/2.34 tff(10773,plain,
% 2.14/2.34 (b(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1786, 10772])).
% 2.14/2.34 tff(10774,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10775,plain,
% 2.14/2.34 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(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(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10776,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10775])).
% 2.14/2.34 tff(10777,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10776, 10774])).
% 2.14/2.34 tff(10778,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(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)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10779,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10778, 10777])).
% 2.14/2.34 tff(10780,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10779, 337, 1, 1275, 1231, 10773, 10771])).
% 2.14/2.34 tff(10781,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(10782,plain,
% 2.14/2.34 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10781, 10731, 1, 1231])).
% 2.14/2.34 tff(10783,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1150, 10782, 10740])).
% 2.14/2.34 tff(10784,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(10785,plain,
% 2.14/2.34 (~r(z, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10784, 1231, 1])).
% 2.14/2.34 tff(10786,plain,
% 2.14/2.34 (b(z, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[80, 10785])).
% 2.14/2.34 tff(10787,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4738, 337, 1, 10786, 1231, 10686])).
% 2.14/2.34 tff(10788,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(10789,plain,
% 2.14/2.34 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10788, 1])).
% 2.14/2.34 tff(10790,plain,
% 2.14/2.34 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[851, 10789])).
% 2.14/2.34 tff(10791,plain,
% 2.14/2.34 (~r(s(s(s(z))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7787, 10790, 10587])).
% 2.14/2.34 tff(10792,plain,
% 2.14/2.34 (b(s(s(s(z))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[48, 10791])).
% 2.14/2.34 tff(10793,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10440, 189, 10790, 2245])).
% 2.14/2.34 tff(10794,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9040, 10793])).
% 2.14/2.34 tff(10795,plain,
% 2.14/2.34 (~r(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10684, 10792, 1])).
% 2.14/2.34 tff(10796,plain,
% 2.14/2.34 (b(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1786, 10795])).
% 2.14/2.34 tff(10797,plain,
% 2.14/2.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10297, 2245, 10790])).
% 2.14/2.34 tff(10798,plain,
% 2.14/2.34 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2268, 10797])).
% 2.14/2.34 tff(10799,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10800,plain,
% 2.14/2.34 (((~b(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(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(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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10801,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10800])).
% 2.14/2.34 tff(10802,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10801, 10799])).
% 2.14/2.34 tff(10803,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(s(z)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10804,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10803, 10802])).
% 2.14/2.34 tff(10805,plain,
% 2.14/2.34 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10804, 337, 1396, 7465, 3242])).
% 2.14/2.34 tff(10806,plain,
% 2.14/2.34 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 10805])).
% 2.14/2.34 tff(10807,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10808,plain,
% 2.14/2.34 (((~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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(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))))), z)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10809,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10808])).
% 2.14/2.34 tff(10810,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10809, 10807])).
% 2.14/2.34 tff(10811,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10812,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10811, 10810])).
% 2.14/2.34 tff(10813,plain,
% 2.14/2.34 (~b(s(s(s(s(s(z))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10812, 337, 1396, 1592, 7465, 3242])).
% 2.14/2.34 tff(10814,plain,
% 2.14/2.34 (r(s(s(s(s(s(z))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 10813])).
% 2.14/2.34 tff(10815,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10816,plain,
% 2.14/2.34 (((~b(s(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)))))) | (~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(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(10817,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[10816])).
% 2.14/2.34 tff(10818,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[10817, 10815])).
% 2.14/2.34 tff(10819,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(10820,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[10819, 10818])).
% 2.14/2.35 tff(10821,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10820, 337, 1396, 1592, 7465, 1342])).
% 2.14/2.35 tff(10822,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10823,plain,
% 2.14/2.35 (~b(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10822, 1396, 1592, 7465])).
% 2.14/2.35 tff(10824,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9005, 43, 1106, 9082, 10385])).
% 2.14/2.35 tff(10825,plain,(b(z, s(s(z))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10826,plain,
% 2.14/2.35 (r(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10825, 10823])).
% 2.14/2.35 tff(10827,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10828,plain,
% 2.14/2.35 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10829,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10828])).
% 2.14/2.35 tff(10830,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[10829, 10827])).
% 2.14/2.35 tff(10831,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(10832,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[10831, 10830])).
% 2.14/2.35 tff(10833,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10832, 189, 10826, 10814, 10806])).
% 2.14/2.35 tff(10834,plain,((~b(s(s(s(s(s(z))))), s(s(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))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10835,plain,
% 2.14/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10834, 10798, 10796, 10794])).
% 2.14/2.35 tff(10836,plain,
% 2.14/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10027, 10835])).
% 2.14/2.35 tff(10837,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10838,plain,
% 2.14/2.35 (((~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(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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10839,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10838])).
% 2.14/2.35 tff(10840,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[10839, 10837])).
% 2.14/2.35 tff(10841,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(10842,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[10841, 10840])).
% 2.14/2.35 tff(10843,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10842, 337, 1, 1275, 1592, 7465, 1396])).
% 2.14/2.35 tff(10844,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10845,plain,
% 2.14/2.35 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10844, 10794, 1, 10796, 10798])).
% 2.14/2.35 tff(10846,plain,
% 2.14/2.35 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1150, 10845])).
% 2.14/2.35 tff(10847,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10127, 189, 10846, 10836])).
% 2.14/2.35 tff(10848,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 10847])).
% 2.14/2.35 tff(10849,plain,
% 2.14/2.35 (~r(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3687, 189, 10846, 10587])).
% 2.14/2.35 tff(10850,plain,
% 2.14/2.35 (b(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2796, 43, 10849, 10690])).
% 2.14/2.35 tff(10851,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7911, 189, 10587, 10836])).
% 2.14/2.35 tff(10852,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10155, 10851])).
% 2.14/2.35 tff(10853,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10854,plain,
% 2.14/2.35 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(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(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10855,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10854])).
% 2.14/2.35 tff(10856,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[10855, 10853])).
% 2.14/2.35 tff(10857,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(10858,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[10857, 10856])).
% 2.14/2.35 tff(10859,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10858, 337, 1, 10792, 10852, 10850, 10848])).
% 2.14/2.35 tff(10860,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10861,plain,
% 2.14/2.35 (~r(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10860, 1])).
% 2.14/2.35 tff(10862,plain,
% 2.14/2.35 (b(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2229, 10861])).
% 2.14/2.35 tff(10863,plain,
% 2.14/2.35 (~b(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10313, 10862, 10792, 1])).
% 2.14/2.35 tff(10864,plain,
% 2.14/2.35 (r(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[80, 10863])).
% 2.14/2.35 tff(10865,plain,
% 2.14/2.35 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10527, 10862, 1, 10792])).
% 2.14/2.35 tff(10866,plain,
% 2.14/2.35 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1150, 10865])).
% 2.14/2.35 tff(10867,plain,
% 2.14/2.35 (~r(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3687, 189, 10866, 10587])).
% 2.14/2.35 tff(10868,plain,
% 2.14/2.35 (b(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2796, 43, 10867, 10690])).
% 2.14/2.35 tff(10869,plain,
% 2.14/2.35 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3698, 337, 10792, 10862, 10868])).
% 2.14/2.35 tff(10870,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2854, 10869])).
% 2.14/2.35 tff(10871,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.14/2.35 tff(10872,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1405, 189, 1339, 1397, 10871])).
% 2.14/2.35 tff(10873,plain,((~r(s(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))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10874,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10873, 10870, 10587])).
% 2.14/2.35 tff(10875,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9040, 10874])).
% 2.14/2.35 tff(10876,plain,
% 2.14/2.35 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10705, 337, 10792, 10862, 10868])).
% 2.14/2.35 tff(10877,plain,
% 2.14/2.35 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4268, 10876])).
% 2.14/2.35 tff(10878,plain,
% 2.14/2.35 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10709, 10877, 10587])).
% 2.14/2.35 tff(10879,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2268, 10878])).
% 2.14/2.35 tff(10880,plain,
% 2.14/2.35 (~b(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10822, 10879, 10796, 10875])).
% 2.14/2.35 tff(10881,plain,
% 2.14/2.35 (r(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10825, 10880])).
% 2.14/2.35 tff(10882,plain,
% 2.14/2.35 (~r(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3378, 10881, 10864])).
% 2.14/2.35 tff(10883,plain,
% 2.14/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10834, 10879, 10796, 10875])).
% 2.14/2.35 tff(10884,plain,
% 2.14/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10027, 10883])).
% 2.14/2.35 tff(10885,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6709, 7912, 10010])).
% 2.14/2.35 tff(10886,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10887,plain,
% 2.14/2.35 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10888,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10887])).
% 2.14/2.35 tff(10889,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[10888, 10886])).
% 2.14/2.35 tff(10890,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(10891,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[10890, 10889])).
% 2.14/2.35 tff(10892,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10891, 337, 3477, 1658, 10885, 3690, 10129])).
% 2.14/2.35 tff(10893,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10894,plain,
% 2.14/2.35 (~b(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10893, 10884, 10587, 10792, 10866])).
% 2.14/2.35 tff(10895,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8207, 10894, 10882])).
% 2.14/2.35 tff(10896,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10897,plain,
% 2.14/2.35 (r(s(z), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[963, 10896])).
% 2.14/2.35 tff(10898,plain,
% 2.14/2.35 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9800])).
% 2.14/2.35 tff(10899,plain,
% 2.14/2.35 (r(s(z), elem!1)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8866, 10898])).
% 2.14/2.35 tff(10900,plain,
% 2.14/2.35 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9804])).
% 2.14/2.35 tff(10901,plain,
% 2.14/2.35 (~b(s(elem!1), elem!1)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6683, 10900])).
% 2.14/2.35 tff(10902,plain,
% 2.14/2.35 (r(s(elem!1), z) <=> r(s(z), z)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9799])).
% 2.14/2.35 tff(10903,plain,
% 2.14/2.35 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.14/2.35 inference(symmetry,[status(thm)],[10902])).
% 2.14/2.35 tff(10904,plain,
% 2.14/2.35 (r(s(elem!1), z)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8866, 10903])).
% 2.14/2.35 tff(10905,plain,
% 2.14/2.35 (~r(s(s(s(z))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3927, 49, 8866])).
% 2.14/2.35 tff(10906,plain,
% 2.14/2.35 (b(s(s(s(z))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1498, 10905])).
% 2.14/2.35 tff(10907,plain,
% 2.14/2.35 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[63])).
% 2.14/2.35 tff(10908,plain,
% 2.14/2.35 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.35 inference(symmetry,[status(thm)],[10907])).
% 2.14/2.35 tff(10909,plain,
% 2.14/2.35 (b(s(s(s(z))), elem!1)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[1659, 10908])).
% 2.14/2.35 tff(10910,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2460, 10909])).
% 2.14/2.35 tff(10911,plain,((~(elem!1 = z)) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10912,plain,
% 2.14/2.35 (b(s(s(s(z))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10911, 10906, 10256])).
% 2.14/2.35 tff(10913,plain,
% 2.14/2.35 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9969])).
% 2.14/2.35 tff(10914,plain,
% 2.14/2.35 (~(s(s(s(z))) = elem!1)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[178, 10913])).
% 2.14/2.35 tff(10915,plain,
% 2.14/2.35 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9822, 9854])).
% 2.14/2.35 tff(10916,plain,
% 2.14/2.35 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10915])).
% 2.14/2.35 tff(10917,plain,
% 2.14/2.35 (~(elem!1 = s(s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[817, 10916])).
% 2.14/2.35 tff(10918,plain,
% 2.14/2.35 (b(elem!1, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4863, 1301, 9825])).
% 2.14/2.35 tff(10919,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9506, 4946, 1735, 327, 8545, 2842, 118, 1481])).
% 2.14/2.35 tff(10920,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[857, 10919, 853])).
% 2.14/2.35 tff(10921,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2079, 189, 1735, 10920, 811])).
% 2.14/2.35 tff(10922,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(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(10923,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[10922, 10918, 9824, 1735, 10917, 118, 10914])).
% 2.14/2.35 tff(10924,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[851, 10923])).
% 2.14/2.35 tff(10925,plain,
% 2.14/2.35 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9614, 10918, 9824, 1735, 118, 10914])).
% 2.14/2.35 tff(10926,plain,
% 2.14/2.35 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1150, 10925])).
% 2.14/2.35 tff(10927,plain,
% 2.14/2.35 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.35 tff(10928,plain,
% 2.14/2.35 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.14/2.35 inference(symmetry,[status(thm)],[10927])).
% 2.14/2.35 tff(10929,plain,
% 2.14/2.35 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9807])).
% 2.14/2.35 tff(10930,plain,
% 2.14/2.35 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.35 inference(symmetry,[status(thm)],[10929])).
% 2.14/2.35 tff(10931,plain,
% 2.14/2.35 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.14/2.35 inference(transitivity,[status(thm)],[10930, 10928])).
% 2.14/2.35 tff(10932,plain,
% 2.14/2.35 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2854, 9105])).
% 2.14/2.35 tff(10933,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(X1, 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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10934,plain,
% 2.14/2.35 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(10935,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[10934])).
% 2.14/2.35 tff(10936,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[10935, 10933])).
% 2.14/2.35 tff(10937,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(10938,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[10937, 10936])).
% 2.14/2.35 tff(10939,plain,
% 2.14/2.35 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10938, 337, 327, 1275, 1396, 2454])).
% 2.14/2.36 tff(10940,plain,
% 2.14/2.36 (~b(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10939, 10932])).
% 2.14/2.36 tff(10941,plain,
% 2.14/2.36 (r(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2301, 10940, 9896])).
% 2.14/2.36 tff(10942,plain,
% 2.14/2.36 (r(s(s(elem!1)), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[10941, 10931])).
% 2.14/2.36 tff(10943,plain,
% 2.14/2.36 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9807, 3070])).
% 2.14/2.36 tff(10944,plain,
% 2.14/2.36 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[10943])).
% 2.14/2.36 tff(10945,plain,
% 2.14/2.36 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9043, 10944])).
% 2.14/2.36 tff(10946,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 2.14/2.36 tff(10947,plain,
% 2.14/2.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(10948,plain,
% 2.14/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(10949,plain,
% 2.14/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[10948, 10947])).
% 2.14/2.36 tff(10950,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10949, 189, 1219, 615, 10946])).
% 2.14/2.36 tff(10951,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(10952,plain,
% 2.14/2.36 (~r(s(s(elem!1)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10951, 10945, 1219])).
% 2.14/2.36 tff(10953,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10952, 10942])).
% 2.14/2.36 tff(10954,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(10955,plain,
% 2.14/2.36 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10954, 10918, 3070, 10926, 2454, 1219, 118, 10924])).
% 2.14/2.36 tff(10956,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2268, 10955])).
% 2.14/2.36 tff(10957,plain,
% 2.14/2.36 (~b(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8258, 337, 10918, 10926, 10924])).
% 2.14/2.36 tff(10958,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2845, 43, 10917, 10957])).
% 2.14/2.36 tff(10959,plain,
% 2.14/2.36 (~r(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2849, 189, 10958, 10956])).
% 2.14/2.36 tff(10960,plain,
% 2.14/2.36 (b(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2301, 10959, 9896])).
% 2.14/2.36 tff(10961,plain,
% 2.14/2.36 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9812])).
% 2.14/2.36 tff(10962,plain,
% 2.14/2.36 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10961])).
% 2.14/2.36 tff(10963,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9808])).
% 2.14/2.36 tff(10964,plain,
% 2.14/2.36 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.14/2.36 inference(symmetry,[status(thm)],[10963])).
% 2.14/2.36 tff(10965,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[2454, 10964])).
% 2.14/2.36 tff(10966,plain,
% 2.14/2.36 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.36 tff(10967,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.36 tff(10968,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[10967])).
% 2.14/2.36 tff(10969,plain,
% 2.14/2.36 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10968])).
% 2.14/2.36 tff(10970,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8161, 337, 10918, 10926, 10924])).
% 2.14/2.36 tff(10971,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[10970, 10969])).
% 2.14/2.36 tff(10972,plain,
% 2.14/2.36 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9817])).
% 2.14/2.36 tff(10973,plain,
% 2.14/2.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[211, 10972])).
% 2.14/2.36 tff(10974,plain,
% 2.14/2.36 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.36 tff(10975,plain,
% 2.14/2.36 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[10974])).
% 2.14/2.36 tff(10976,plain,
% 2.14/2.36 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10975])).
% 2.14/2.36 tff(10977,plain,
% 2.14/2.36 (~b(elem!1, z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[6600, 10976])).
% 2.14/2.36 tff(10978,plain,
% 2.14/2.36 ((s(z) = z) <=> (s(z) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.36 tff(10979,plain,
% 2.14/2.36 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.14/2.36 inference(transitivity,[status(thm)],[10978, 119])).
% 2.14/2.36 tff(10980,plain,
% 2.14/2.36 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10979])).
% 2.14/2.36 tff(10981,plain,
% 2.14/2.36 (~(elem!1 = s(z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[74, 10980])).
% 2.14/2.36 tff(10982,plain,
% 2.14/2.36 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9821])).
% 2.14/2.36 tff(10983,plain,
% 2.14/2.36 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[10982])).
% 2.14/2.36 tff(10984,plain,
% 2.14/2.36 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(z, s(s(s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10983])).
% 2.14/2.36 tff(10985,plain,
% 2.14/2.36 (~b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[10957, 10984])).
% 2.14/2.36 tff(10986,plain,
% 2.14/2.36 (r(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1786, 10985])).
% 2.14/2.36 tff(10987,plain,
% 2.14/2.36 (z = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5552, 271, 247, 1301, 1790, 172, 1115, 82, 4858])).
% 2.14/2.36 tff(10988,plain,
% 2.14/2.36 (s(elem!1) = s(z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[60, 10987])).
% 2.14/2.36 tff(10989,plain,
% 2.14/2.36 (s(s(elem!1)) = s(s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10988])).
% 2.14/2.36 tff(10990,plain,
% 2.14/2.36 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10989])).
% 2.14/2.36 tff(10991,plain,
% 2.14/2.36 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[10990])).
% 2.14/2.36 tff(10992,plain,
% 2.14/2.36 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10991])).
% 2.14/2.36 tff(10993,plain,
% 2.14/2.36 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[10992])).
% 2.14/2.36 tff(10994,plain,
% 2.14/2.36 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10988])).
% 2.14/2.36 tff(10995,plain,
% 2.14/2.36 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[56])).
% 2.14/2.36 tff(10996,plain,
% 2.14/2.36 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[10995])).
% 2.14/2.36 tff(10997,plain,
% 2.14/2.36 (r(s(elem!1), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[273, 10996])).
% 2.14/2.36 tff(10998,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1255, 10997])).
% 2.14/2.36 tff(10999,plain,((~(z = elem!1)) | r(s(elem!1), z) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(11000,plain,
% 2.14/2.36 (r(s(elem!1), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10999, 10987, 271])).
% 2.14/2.36 tff(11001,plain,
% 2.14/2.36 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1227, 11000, 147])).
% 2.14/2.36 tff(11002,plain,
% 2.14/2.36 (b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[579, 11001, 428])).
% 2.14/2.36 tff(11003,plain,
% 2.14/2.36 (b(s(z), s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11002, 10994])).
% 2.14/2.36 tff(11004,plain,
% 2.14/2.36 (b(s(z), s(s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11003, 10993])).
% 2.14/2.36 tff(11005,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10990])).
% 2.14/2.36 tff(11006,plain,
% 2.14/2.36 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[2650])).
% 2.14/2.36 tff(11007,plain,
% 2.14/2.36 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[266, 11006])).
% 2.14/2.36 tff(11008,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[638, 11007])).
% 2.14/2.36 tff(11009,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(11010,plain,
% 2.14/2.36 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11009, 11002, 266])).
% 2.14/2.36 tff(11011,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10988])).
% 2.14/2.36 tff(11012,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[11011])).
% 2.14/2.36 tff(11013,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10990])).
% 2.14/2.36 tff(11014,plain,
% 2.14/2.36 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.14/2.36 inference(symmetry,[status(thm)],[11013])).
% 2.14/2.36 tff(11015,plain,
% 2.14/2.36 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.36 inference(transitivity,[status(thm)],[11014, 11012])).
% 2.14/2.36 tff(11016,plain,
% 2.14/2.36 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[11015])).
% 2.14/2.36 tff(11017,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10987])).
% 2.14/2.36 tff(11018,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[3104, 11017])).
% 2.14/2.36 tff(11019,plain,
% 2.14/2.36 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10988])).
% 2.14/2.36 tff(11020,plain,
% 2.14/2.36 (r(s(z), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[271, 11019])).
% 2.14/2.36 tff(11021,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2079, 189, 11020, 11018])).
% 2.14/2.36 tff(11022,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[851, 11021])).
% 2.14/2.36 tff(11023,plain,
% 2.14/2.36 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2089, 11018, 11020])).
% 2.14/2.36 tff(11024,plain,
% 2.14/2.36 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1150, 11023])).
% 2.14/2.36 tff(11025,plain,
% 2.14/2.36 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10990])).
% 2.14/2.36 tff(11026,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[11025])).
% 2.14/2.36 tff(11027,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[11026])).
% 2.14/2.36 tff(11028,plain,
% 2.14/2.36 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10987])).
% 2.14/2.36 tff(11029,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1115, 11028])).
% 2.14/2.36 tff(11030,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11029, 11027])).
% 2.14/2.36 tff(11031,plain,
% 2.14/2.36 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[10987])).
% 2.14/2.36 tff(11032,plain,
% 2.14/2.36 (r(elem!1, s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[147, 11031])).
% 2.14/2.36 tff(11033,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9991, 11032, 10987, 11030])).
% 2.14/2.36 tff(11034,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[524, 11033])).
% 2.14/2.36 tff(11035,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11036,plain,
% 2.14/2.36 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(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)))) <=> ((~b(s(z), s(s(s(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(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11037,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[11036])).
% 2.14/2.36 tff(11038,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[11037, 11035])).
% 2.14/2.36 tff(11039,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(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))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(11040,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11039, 11038])).
% 2.14/2.36 tff(11041,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11040, 337, 3243, 1275, 1231, 1658, 10691])).
% 2.14/2.36 tff(11042,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(11043,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11042, 11034, 11024, 11022, 11004])).
% 2.14/2.36 tff(11044,plain,
% 2.14/2.36 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11043, 11016])).
% 2.14/2.36 tff(11045,plain,
% 2.14/2.36 (r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[363, 11044, 172])).
% 2.14/2.36 tff(11046,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[358, 11045, 271])).
% 2.14/2.36 tff(11047,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[350, 11046, 11010])).
% 2.14/2.36 tff(11048,plain,
% 2.14/2.36 (b(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11047, 11005])).
% 2.14/2.36 tff(11049,plain,
% 2.14/2.36 (elem!1 = z),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4411, 10987])).
% 2.14/2.36 tff(11050,plain,
% 2.14/2.36 (b(elem!1, s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4863, 11049, 1301])).
% 2.14/2.36 tff(11051,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11052,plain,
% 2.14/2.36 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~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(z), s(s(s(s(z)))))) | (~b(elem!1, 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))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11053,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~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(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[11052])).
% 2.14/2.36 tff(11054,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~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(X1, 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[11053, 11051])).
% 2.14/2.36 tff(11055,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~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)))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(11056,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11055, 11054])).
% 2.14/2.36 tff(11057,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11056, 337, 11050, 11034, 11024, 11022, 11048, 11004])).
% 2.14/2.36 tff(11058,plain,(b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(11059,plain,
% 2.14/2.36 (b(z, s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11058, 10986, 10981, 10977, 266, 1301, 10973, 10971])).
% 2.14/2.36 tff(11060,plain,
% 2.14/2.36 (b(elem!1, s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11059, 10966])).
% 2.14/2.36 tff(11061,plain,
% 2.14/2.36 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[345, 11060, 10918, 10965])).
% 2.14/2.36 tff(11062,plain,
% 2.14/2.36 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11061, 10962])).
% 2.14/2.36 tff(11063,plain,
% 2.14/2.36 (r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[579, 11062, 9820])).
% 2.14/2.36 tff(11064,plain,
% 2.14/2.36 (r(s(z), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[10074, 11063, 3070])).
% 2.14/2.36 tff(11065,plain,
% 2.14/2.36 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5133, 10956, 1301, 10986])).
% 2.14/2.36 tff(11066,plain,
% 2.14/2.36 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[548, 11065])).
% 2.14/2.36 tff(11067,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, 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(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11068,plain,
% 2.14/2.36 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11069,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[11068])).
% 2.14/2.36 tff(11070,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[11069, 11067])).
% 2.14/2.36 tff(11071,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(11072,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[11071, 11070])).
% 2.14/2.36 tff(11073,plain,
% 2.14/2.36 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[11072, 337, 10918, 10926, 11066, 10960, 2454])).
% 2.14/2.36 tff(11074,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4268, 11073])).
% 2.14/2.36 tff(11075,plain,
% 2.14/2.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(11076,plain,
% 2.14/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11077,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11076, 11075])).
% 2.14/2.37 tff(11078,plain,
% 2.14/2.37 (~r(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11077, 189, 11074, 11064])).
% 2.14/2.37 tff(11079,plain,
% 2.14/2.37 (b(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2229, 11078])).
% 2.14/2.37 tff(11080,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), 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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11081,plain,
% 2.14/2.37 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11082,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11081])).
% 2.14/2.37 tff(11083,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11082, 11080])).
% 2.14/2.37 tff(11084,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11085,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11084, 11083])).
% 2.14/2.37 tff(11086,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11085, 337, 10918, 10926, 10924, 11079, 10960])).
% 2.14/2.37 tff(11087,plain,((~b(z, s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(z))) | b(s(elem!1), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11088,plain,
% 2.14/2.37 (~b(z, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11087, 9799, 10912, 10904, 49, 10901, 10899])).
% 2.14/2.37 tff(11089,plain,
% 2.14/2.37 (r(z, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[80, 11088])).
% 2.14/2.37 tff(11090,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[56])).
% 2.14/2.37 tff(11091,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.14/2.37 inference(symmetry,[status(thm)],[11090])).
% 2.14/2.37 tff(11092,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2089, 1141, 1735])).
% 2.14/2.37 tff(11093,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[857, 11092, 10097])).
% 2.14/2.37 tff(11094,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), z)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11093, 11091])).
% 2.14/2.37 tff(11095,plain,
% 2.14/2.37 (~r(z, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1580, 1141, 173])).
% 2.14/2.37 tff(11096,plain,
% 2.14/2.37 (b(z, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1786, 11095])).
% 2.14/2.37 tff(11097,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1795, 11096, 1659, 4127])).
% 2.14/2.37 tff(11098,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11097, 11094])).
% 2.14/2.37 tff(11099,plain,((~r(s(z), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11100,plain,
% 2.14/2.37 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11099, 9800, 10906, 11089, 10899, 49])).
% 2.14/2.37 tff(11101,plain,
% 2.14/2.37 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1150, 11100])).
% 2.14/2.37 tff(11102,plain,
% 2.14/2.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8180, 811, 173, 1770])).
% 2.14/2.37 tff(11103,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[548, 11102, 8544])).
% 2.14/2.37 tff(11104,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11105,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11104, 173, 118])).
% 2.14/2.37 tff(11106,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[851, 11105])).
% 2.14/2.37 tff(11107,plain,
% 2.14/2.37 (~b(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8987, 337, 1275, 11106, 1396])).
% 2.14/2.37 tff(11108,plain,
% 2.14/2.37 (r(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2229, 11107])).
% 2.14/2.37 tff(11109,plain,
% 2.14/2.37 (~r(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2253, 11108, 173])).
% 2.14/2.37 tff(11110,plain,
% 2.14/2.37 (~b(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1239, 337, 1275, 11106, 1396])).
% 2.14/2.37 tff(11111,plain,
% 2.14/2.37 (r(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8207, 11110])).
% 2.14/2.37 tff(11112,plain,
% 2.14/2.37 (~b(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8213, 11111, 118, 173])).
% 2.14/2.37 tff(11113,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2242, 11112, 11109])).
% 2.14/2.37 tff(11114,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11115,plain,
% 2.14/2.37 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11114, 11101, 49, 11089])).
% 2.14/2.37 tff(11116,plain,
% 2.14/2.37 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2268, 11115])).
% 2.14/2.37 tff(11117,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[10265, 9854])).
% 2.14/2.37 tff(11118,plain,
% 2.14/2.37 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11117])).
% 2.14/2.37 tff(11119,plain,
% 2.14/2.37 (~(elem!1 = s(s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[817, 11118])).
% 2.14/2.37 tff(11120,plain,
% 2.14/2.37 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[10589])).
% 2.14/2.37 tff(11121,plain,
% 2.14/2.37 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9800])).
% 2.14/2.37 tff(11122,plain,
% 2.14/2.37 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11121, 11120])).
% 2.14/2.37 tff(11123,plain,
% 2.14/2.37 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[10589])).
% 2.14/2.37 tff(11124,plain,
% 2.14/2.37 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.14/2.37 inference(symmetry,[status(thm)],[11123])).
% 2.14/2.37 tff(11125,plain,
% 2.14/2.37 (r(s(s(s(elem!1))), s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[49, 11124])).
% 2.14/2.37 tff(11126,plain,
% 2.14/2.37 (~r(z, s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[223, 11089, 11125])).
% 2.14/2.37 tff(11127,plain,
% 2.14/2.37 (b(z, s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[146, 11126])).
% 2.14/2.37 tff(11128,plain,
% 2.14/2.37 (b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11127, 11122])).
% 2.14/2.37 tff(11129,plain,
% 2.14/2.37 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[10261])).
% 2.14/2.37 tff(11130,plain,
% 2.14/2.37 (~(elem!1 = s(s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[31, 11129])).
% 2.14/2.37 tff(11131,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 2.14/2.37 tff(11132,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11133,plain,
% 2.14/2.37 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11134,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11133])).
% 2.14/2.37 tff(11135,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11134, 11132])).
% 2.14/2.37 tff(11136,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11137,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11136, 11135])).
% 2.14/2.37 tff(11138,plain,
% 2.14/2.37 (~b(elem!1, s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11137, 337, 5123, 2454, 10629])).
% 2.14/2.37 tff(11139,plain,
% 2.14/2.37 (r(elem!1, s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9064, 11138, 11131])).
% 2.14/2.37 tff(11140,plain,
% 2.14/2.37 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(s(s(s(s(z)))))) | (s(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))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7931, 10141])).
% 2.14/2.37 tff(11141,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11140, 1339, 10351, 10010, 1659, 4222])).
% 2.14/2.37 tff(11142,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6726, 11141, 10026])).
% 2.14/2.37 tff(11143,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11144,plain,
% 2.14/2.37 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11145,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11144])).
% 2.14/2.37 tff(11146,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11145, 11143])).
% 2.14/2.37 tff(11147,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11148,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11147, 11146])).
% 2.14/2.37 tff(11149,plain,
% 2.14/2.37 (~b(s(s(z)), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11148, 337, 5123, 2454, 10629])).
% 2.14/2.37 tff(11150,plain,
% 2.14/2.37 (r(s(s(z)), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2301, 11149, 4103])).
% 2.14/2.37 tff(11151,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9910, 189, 1169, 4222, 11150])).
% 2.14/2.37 tff(11152,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11153,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11152, 1339, 2454, 4103, 10629, 4222])).
% 2.14/2.37 tff(11154,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[857, 11153, 853])).
% 2.14/2.37 tff(11155,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, 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(X1, 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)))), elem!1)) | (~b(elem!1, 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))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11156,plain,
% 2.14/2.37 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, 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))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11157,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, 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)))), elem!1)) | (~b(elem!1, 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)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11156])).
% 2.14/2.37 tff(11158,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, 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)))), elem!1)) | (~b(elem!1, 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))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11157, 11155])).
% 2.14/2.37 tff(11159,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11160,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, 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)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11159, 11158])).
% 2.14/2.37 tff(11161,plain,
% 2.14/2.37 (~b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11160, 337, 1275, 1603, 4942, 3242])).
% 2.14/2.37 tff(11162,plain,
% 2.14/2.37 (r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 11161])).
% 2.14/2.37 tff(11163,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11164,plain,
% 2.14/2.37 (((~b(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11165,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(z))))), s(s(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[11164])).
% 2.14/2.37 tff(11166,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(z))))), s(s(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[11165, 11163])).
% 2.14/2.37 tff(11167,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11168,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11167, 11166])).
% 2.14/2.37 tff(11169,plain,
% 2.14/2.37 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11168, 337, 1603, 4942, 3242])).
% 2.14/2.37 tff(11170,plain,
% 2.14/2.37 (r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[10056, 11169, 10631])).
% 2.14/2.37 tff(11171,plain,
% 2.14/2.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(11172,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(11173,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[11172, 11171])).
% 2.14/2.37 tff(11174,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11173, 189, 1735, 11170, 11162])).
% 2.14/2.37 tff(11175,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(11176,plain,
% 2.14/2.37 (~b(elem!1, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[11175, 11154, 1735, 1275, 11142, 10631])).
% 2.14/2.37 tff(11177,plain,
% 2.14/2.37 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2845, 43, 2842, 11176])).
% 2.14/2.38 tff(11178,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9869, 189, 11177, 4222, 11139])).
% 2.14/2.38 tff(11179,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(11180,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11179, 11116, 11130, 10912, 11128, 11119, 10899, 11101, 10609, 10267, 10264, 10906])).
% 2.14/2.38 tff(11181,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[548, 11180])).
% 2.14/2.38 tff(11182,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11104, 11089, 49])).
% 2.14/2.38 tff(11183,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[851, 11182])).
% 2.14/2.38 tff(11184,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11185,plain,
% 2.14/2.38 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11186,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11185])).
% 2.14/2.38 tff(11187,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11186, 11184])).
% 2.14/2.38 tff(11188,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11189,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11188, 11187])).
% 2.14/2.38 tff(11190,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11189, 337, 1275, 2, 1231, 4942, 10629])).
% 2.14/2.38 tff(11191,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(11192,plain,
% 2.14/2.38 (~b(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11191, 11101, 11181, 11183, 11128])).
% 2.14/2.38 tff(11193,plain,
% 2.14/2.38 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2845, 43, 11119, 11192])).
% 2.14/2.38 tff(11194,plain,
% 2.14/2.38 (~r(elem!1, s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9869, 189, 11193, 11116])).
% 2.14/2.38 tff(11195,plain,
% 2.14/2.38 (b(elem!1, s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9064, 11194, 11130])).
% 2.14/2.38 tff(11196,plain,
% 2.14/2.38 (~r(s(s(z)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2253, 2245, 173])).
% 2.14/2.38 tff(11197,plain,
% 2.14/2.38 (b(s(s(z)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2242, 11196])).
% 2.14/2.38 tff(11198,plain,
% 2.14/2.38 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2866, 11197, 118, 173])).
% 2.14/2.38 tff(11199,plain,
% 2.14/2.38 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2854, 11198])).
% 2.14/2.38 tff(11200,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7348, 189, 118, 11199, 2245])).
% 2.14/2.38 tff(11201,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(11202,plain,
% 2.14/2.38 (~r(s(s(z)), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11201, 49, 11089])).
% 2.14/2.38 tff(11203,plain,
% 2.14/2.38 (b(s(s(z)), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2229, 11202])).
% 2.14/2.38 tff(11204,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11205,plain,
% 2.14/2.38 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11206,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11205])).
% 2.14/2.38 tff(11207,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11206, 11204])).
% 2.14/2.38 tff(11208,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11209,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11208, 11207])).
% 2.14/2.38 tff(11210,plain,
% 2.14/2.38 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11209, 337, 11101, 11181, 11203, 11195, 11128])).
% 2.14/2.38 tff(11211,plain,
% 2.14/2.38 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2854, 11210])).
% 2.14/2.38 tff(11212,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11213,plain,
% 2.14/2.38 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11214,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11213])).
% 2.14/2.38 tff(11215,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), s(z))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11214, 11212])).
% 2.14/2.38 tff(11216,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11217,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11216, 11215])).
% 2.14/2.38 tff(11218,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11217, 337, 11101, 11183, 11203])).
% 2.14/2.38 tff(11219,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9040, 11218])).
% 2.14/2.38 tff(11220,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3226, 189, 11219, 11211])).
% 2.14/2.38 tff(11221,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[524, 11220])).
% 2.14/2.38 tff(11222,plain,
% 2.14/2.38 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9799])).
% 2.14/2.38 tff(11223,plain,
% 2.14/2.38 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11222, 366])).
% 2.14/2.38 tff(11224,plain,
% 2.14/2.38 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.38 inference(symmetry,[status(thm)],[11223])).
% 2.14/2.38 tff(11225,plain,
% 2.14/2.38 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11224, 9814])).
% 2.14/2.38 tff(11226,plain,
% 2.14/2.38 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11225])).
% 2.14/2.38 tff(11227,plain,
% 2.14/2.38 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[211, 11226])).
% 2.14/2.38 tff(11228,plain,
% 2.14/2.38 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9799])).
% 2.14/2.38 tff(11229,plain,
% 2.14/2.38 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[11228])).
% 2.14/2.38 tff(11230,plain,
% 2.14/2.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10589])).
% 2.14/2.38 tff(11231,plain,
% 2.14/2.38 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11230])).
% 2.14/2.38 tff(11232,plain,
% 2.14/2.38 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11231, 11229])).
% 2.14/2.38 tff(11233,plain,
% 2.14/2.38 ((~b(s(z), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11232])).
% 2.14/2.38 tff(11234,plain,
% 2.14/2.38 (~b(s(z), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10085, 337, 11101, 11181, 11183])).
% 2.14/2.38 tff(11235,plain,
% 2.14/2.38 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11234, 11233])).
% 2.14/2.38 tff(11236,plain,
% 2.14/2.38 (r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[579, 11235, 11227])).
% 2.14/2.38 tff(11237,plain,
% 2.14/2.38 (r(s(z), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10074, 11236, 9799])).
% 2.14/2.38 tff(11238,plain,
% 2.14/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10019, 11237, 11221, 11181, 11101])).
% 2.14/2.38 tff(11239,plain,
% 2.14/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6726, 11238, 10026])).
% 2.14/2.38 tff(11240,plain,
% 2.14/2.38 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3566, 189, 11239, 11116])).
% 2.14/2.38 tff(11241,plain,
% 2.14/2.38 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 11240])).
% 2.14/2.38 tff(11242,plain,
% 2.14/2.38 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10051, 189, 11193, 11239])).
% 2.14/2.38 tff(11243,plain,
% 2.14/2.38 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10056, 11242, 10609])).
% 2.14/2.38 tff(11244,plain,
% 2.14/2.38 (~r(s(s(z)), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2849, 189, 11193, 11116])).
% 2.14/2.38 tff(11245,plain,
% 2.14/2.38 (b(s(s(z)), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2301, 11244, 10264])).
% 2.14/2.38 tff(11246,plain,
% 2.14/2.38 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10606])).
% 2.14/2.38 tff(11247,plain,
% 2.14/2.38 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10047, 11246])).
% 2.14/2.38 tff(11248,plain,
% 2.14/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11249,plain,
% 2.14/2.38 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11250,plain,
% 2.14/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11249])).
% 2.14/2.38 tff(11251,plain,
% 2.14/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11250, 11248])).
% 2.14/2.38 tff(11252,plain,
% 2.14/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11253,plain,
% 2.14/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11252, 11251])).
% 2.14/2.38 tff(11254,plain,
% 2.14/2.38 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11253, 189, 11193, 11239])).
% 2.14/2.38 tff(11255,plain,
% 2.14/2.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11256,plain,
% 2.14/2.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11257,plain,
% 2.14/2.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11256, 11255])).
% 2.14/2.38 tff(11258,plain,
% 2.14/2.38 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11257, 43])).
% 2.14/2.38 tff(11259,plain,
% 2.14/2.38 (b(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11258, 11254, 11247])).
% 2.14/2.38 tff(11260,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11261,plain,
% 2.14/2.38 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11262,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~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(X1, 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(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[11261])).
% 2.14/2.38 tff(11263,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~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(X1, 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(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[11262, 11260])).
% 2.14/2.38 tff(11264,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(11265,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[11264, 11263])).
% 2.14/2.38 tff(11266,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11265, 337, 11259, 11245, 11243, 11241])).
% 2.14/2.38 tff(11267,plain,(b(s(s(s(z))), s(z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(11268,plain,
% 2.14/2.38 (b(s(s(s(z))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11267, 10896])).
% 2.14/2.38 tff(11269,plain,
% 2.14/2.38 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1150, 5641])).
% 2.14/2.38 tff(11270,plain,
% 2.14/2.38 (~r(s(z), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3687, 189, 11269, 1339])).
% 2.14/2.38 tff(11271,plain,
% 2.14/2.38 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2796, 43, 11270])).
% 2.14/2.38 tff(11272,plain,
% 2.14/2.38 (b(s(z), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11271, 2781])).
% 2.14/2.38 tff(11273,plain,
% 2.14/2.38 (b(s(s(s(z))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[11267, 6683])).
% 2.14/2.38 tff(11274,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11275,plain,
% 2.14/2.38 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(z)))) <=> ((~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(11276,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11275])).
% 2.14/2.39 tff(11277,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11276, 11274])).
% 2.14/2.39 tff(11278,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(z))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(11279,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11278, 11277])).
% 2.14/2.39 tff(11280,plain,
% 2.14/2.39 (~b(s(z), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11279, 337, 11273, 11272])).
% 2.14/2.39 tff(11281,plain,
% 2.14/2.39 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[230])).
% 2.14/2.39 tff(11282,plain,
% 2.14/2.39 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 2.14/2.39 inference(symmetry,[status(thm)],[11281])).
% 2.14/2.39 tff(11283,plain,
% 2.14/2.39 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11282])).
% 2.14/2.39 tff(11284,assumption,(~b(s(z), s(z))), introduced(assumption)).
% 2.14/2.39 tff(11285,plain,
% 2.14/2.39 (~b(s(z), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11284, 11283])).
% 2.14/2.39 tff(11286,plain,
% 2.14/2.39 (~b(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6686, 230, 6683])).
% 2.14/2.39 tff(11287,plain,
% 2.14/2.39 (r(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1759, 11286, 1900])).
% 2.14/2.39 tff(11288,plain,
% 2.14/2.39 (~r(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2896, 11287, 8866])).
% 2.14/2.39 tff(11289,plain,
% 2.14/2.39 (s(z) = elem!1),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[727, 1878, 4381])).
% 2.14/2.39 tff(11290,plain,
% 2.14/2.39 (s(s(z)) = s(elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11291,plain,
% 2.14/2.39 (s(s(s(z))) = s(s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11290])).
% 2.14/2.39 tff(11292,plain,
% 2.14/2.39 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11291])).
% 2.14/2.39 tff(11293,plain,
% 2.14/2.39 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11292])).
% 2.14/2.39 tff(11294,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11295,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11294, 11293])).
% 2.14/2.39 tff(11296,plain,
% 2.14/2.39 (elem!1 = s(z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[249, 11289])).
% 2.14/2.39 tff(11297,plain,
% 2.14/2.39 ((elem!1 = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11290])).
% 2.14/2.39 tff(11298,plain,
% 2.14/2.39 ((elem!1 = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.14/2.39 inference(transitivity,[status(thm)],[11297, 975])).
% 2.14/2.39 tff(11299,plain,
% 2.14/2.39 ((~(elem!1 = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11298])).
% 2.14/2.39 tff(11300,plain,
% 2.14/2.39 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11301,plain,
% 2.14/2.39 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11300])).
% 2.14/2.39 tff(11302,plain,
% 2.14/2.39 (~(elem!1 = s(s(z)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[8206, 11301])).
% 2.14/2.39 tff(11303,plain,
% 2.14/2.39 (~(s(elem!1) = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11302, 11299])).
% 2.14/2.39 tff(11304,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11292])).
% 2.14/2.39 tff(11305,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11304])).
% 2.14/2.39 tff(11306,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11290])).
% 2.14/2.39 tff(11307,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11306, 4627])).
% 2.14/2.39 tff(11308,plain,
% 2.14/2.39 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11307])).
% 2.14/2.39 tff(11309,plain,
% 2.14/2.39 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2263, 11308])).
% 2.14/2.39 tff(11310,plain,
% 2.14/2.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11309, 11305])).
% 2.14/2.39 tff(11311,plain,
% 2.14/2.39 ((s(z) = z) <=> (elem!1 = z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11312,plain,
% 2.14/2.39 ((s(z) = z) <=> (z = elem!1)),
% 2.14/2.39 inference(transitivity,[status(thm)],[11311, 62])).
% 2.14/2.39 tff(11313,plain,
% 2.14/2.39 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11312])).
% 2.14/2.39 tff(11314,plain,
% 2.14/2.39 (~(z = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[74, 11313])).
% 2.14/2.39 tff(11315,plain,
% 2.14/2.39 (~b(z, elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[935, 69, 11296])).
% 2.14/2.39 tff(11316,plain,
% 2.14/2.39 (r(z, elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[921, 11315, 11314])).
% 2.14/2.39 tff(11317,plain,
% 2.14/2.39 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11294])).
% 2.14/2.39 tff(11318,plain,
% 2.14/2.39 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11293])).
% 2.14/2.39 tff(11319,plain,
% 2.14/2.39 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11318, 11317])).
% 2.14/2.39 tff(11320,plain,
% 2.14/2.39 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11319])).
% 2.14/2.39 tff(11321,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11292])).
% 2.14/2.39 tff(11322,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2023, 8520, 81])).
% 2.14/2.39 tff(11323,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1792, 11322])).
% 2.14/2.39 tff(11324,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), z)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11323, 11321])).
% 2.14/2.39 tff(11325,plain,
% 2.14/2.39 (~r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[8078, 8520, 81])).
% 2.14/2.39 tff(11326,plain,
% 2.14/2.39 (~r(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3047, 11296, 11325])).
% 2.14/2.39 tff(11327,plain,
% 2.14/2.39 (b(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[146, 11326])).
% 2.14/2.39 tff(11328,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11292])).
% 2.14/2.39 tff(11329,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11330,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[8520, 11329])).
% 2.14/2.39 tff(11331,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11330, 11328])).
% 2.14/2.39 tff(11332,plain,
% 2.14/2.39 (~b(z, elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[935, 11296, 69])).
% 2.14/2.39 tff(11333,plain,
% 2.14/2.39 (~(s(elem!1) = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7830, 11327, 11332])).
% 2.14/2.39 tff(11334,plain,
% 2.14/2.39 (~(elem!1 = s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[980, 11333])).
% 2.14/2.39 tff(11335,plain,
% 2.14/2.39 (s(s(elem!1)) = s(s(s(z)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11291])).
% 2.14/2.39 tff(11336,plain,
% 2.14/2.39 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11335])).
% 2.14/2.39 tff(11337,plain,
% 2.14/2.39 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11336])).
% 2.14/2.39 tff(11338,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11290])).
% 2.14/2.39 tff(11339,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11338, 11337])).
% 2.14/2.39 tff(11340,plain,
% 2.14/2.39 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11290])).
% 2.14/2.39 tff(11341,plain,
% 2.14/2.39 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11340])).
% 2.14/2.39 tff(11342,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11335])).
% 2.14/2.39 tff(11343,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11342, 11341])).
% 2.14/2.39 tff(11344,plain,
% 2.14/2.39 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(s(z))), s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11343])).
% 2.14/2.39 tff(11345,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11289])).
% 2.14/2.39 tff(11346,plain,
% 2.14/2.39 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11345])).
% 2.14/2.39 tff(11347,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[8519, 11346])).
% 2.14/2.39 tff(11348,plain,
% 2.14/2.39 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[674])).
% 2.14/2.39 tff(11349,plain,
% 2.14/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[617])).
% 2.14/2.39 tff(11350,plain,
% 2.14/2.39 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[617, 432])).
% 2.14/2.39 tff(11351,plain,
% 2.14/2.39 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11350])).
% 2.14/2.39 tff(11352,plain,
% 2.14/2.39 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11351])).
% 2.14/2.39 tff(11353,plain,
% 2.14/2.39 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[433])).
% 2.14/2.39 tff(11354,plain,
% 2.14/2.39 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11353, 681])).
% 2.14/2.39 tff(11355,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11354])).
% 2.14/2.39 tff(11356,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11355])).
% 2.14/2.39 tff(11357,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) | (~(s(z) = elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[694, 116])).
% 2.14/2.39 tff(11358,plain,
% 2.14/2.39 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11357, 245])).
% 2.14/2.39 tff(11359,plain,
% 2.14/2.39 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11358, 11356])).
% 2.14/2.39 tff(11360,plain,
% 2.14/2.39 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11359, 11352])).
% 2.14/2.39 tff(11361,plain,
% 2.14/2.39 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[617])).
% 2.14/2.39 tff(11362,plain,
% 2.14/2.39 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11361])).
% 2.14/2.39 tff(11363,plain,
% 2.14/2.39 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[672, 11362])).
% 2.14/2.39 tff(11364,plain,
% 2.14/2.39 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11363])).
% 2.14/2.39 tff(11365,plain,
% 2.14/2.39 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[433])).
% 2.14/2.39 tff(11366,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11365])).
% 2.14/2.39 tff(11367,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11366, 9814])).
% 2.14/2.39 tff(11368,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11367])).
% 2.14/2.39 tff(11369,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[454])).
% 2.14/2.39 tff(11370,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11369, 7335])).
% 2.14/2.39 tff(11371,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11370])).
% 2.14/2.39 tff(11372,plain,
% 2.14/2.39 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11371])).
% 2.14/2.39 tff(11373,plain,
% 2.14/2.39 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2263, 11372])).
% 2.14/2.39 tff(11374,plain,
% 2.14/2.39 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11373, 11368])).
% 2.14/2.39 tff(11375,plain,
% 2.14/2.39 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[454, 431])).
% 2.14/2.39 tff(11376,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[11375])).
% 2.14/2.39 tff(11377,plain,
% 2.14/2.39 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[454, 431])).
% 2.14/2.39 tff(11378,plain,
% 2.14/2.39 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11377])).
% 2.14/2.39 tff(11379,plain,
% 2.14/2.39 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[245])).
% 2.14/2.39 tff(11380,plain,
% 2.14/2.39 (b(s(s(s(z))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[1658, 11379])).
% 2.14/2.39 tff(11381,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[431])).
% 2.14/2.39 tff(11382,plain,
% 2.14/2.39 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(symmetry,[status(thm)],[11381])).
% 2.14/2.39 tff(11383,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2454, 11382])).
% 2.14/2.39 tff(11384,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.39 tff(11385,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11384, 11383])).
% 2.14/2.39 tff(11386,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(11387,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11386, 11380, 245])).
% 2.14/2.39 tff(11388,plain,
% 2.14/2.39 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[454])).
% 2.14/2.39 tff(11389,plain,
% 2.14/2.39 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11388, 2114])).
% 2.14/2.39 tff(11390,plain,
% 2.14/2.39 ((elem!1 = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.14/2.39 inference(symmetry,[status(thm)],[11389])).
% 2.14/2.39 tff(11391,plain,
% 2.14/2.39 ((elem!1 = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11390, 4587])).
% 2.14/2.39 tff(11392,plain,
% 2.14/2.39 ((~(elem!1 = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11391])).
% 2.14/2.39 tff(11393,plain,
% 2.14/2.39 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[245])).
% 2.14/2.39 tff(11394,plain,
% 2.14/2.39 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11393])).
% 2.14/2.39 tff(11395,plain,
% 2.14/2.39 (~(elem!1 = s(s(z)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[8206, 11394])).
% 2.14/2.39 tff(11396,plain,
% 2.14/2.39 (~(elem!1 = s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11395, 11392])).
% 2.14/2.39 tff(11397,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[432])).
% 2.14/2.39 tff(11398,plain,
% 2.14/2.39 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11397])).
% 2.14/2.39 tff(11399,plain,
% 2.14/2.39 (~b(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[229, 11398])).
% 2.14/2.39 tff(11400,plain,
% 2.14/2.39 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.14/2.39 inference(transitivity,[status(thm)],[623, 277])).
% 2.14/2.39 tff(11401,plain,
% 2.14/2.39 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11400])).
% 2.14/2.39 tff(11402,plain,
% 2.14/2.39 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[211, 11401])).
% 2.14/2.39 tff(11403,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[350, 11402, 11399])).
% 2.14/2.39 tff(11404,plain,
% 2.14/2.39 ((s(z) = z) <=> (elem!1 = z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[245])).
% 2.14/2.39 tff(11405,plain,
% 2.14/2.39 ((s(z) = z) <=> (z = elem!1)),
% 2.14/2.39 inference(transitivity,[status(thm)],[11404, 62])).
% 2.14/2.39 tff(11406,plain,
% 2.14/2.39 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11405])).
% 2.14/2.39 tff(11407,plain,
% 2.14/2.39 (~(z = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[74, 11406])).
% 2.14/2.39 tff(11408,plain,
% 2.14/2.39 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[430])).
% 2.14/2.39 tff(11409,plain,
% 2.14/2.39 (b(s(s(elem!1)), z)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[1659, 11408])).
% 2.14/2.39 tff(11410,plain,
% 2.14/2.39 ((s(z) = z) <=> (elem!1 = z)),
% 2.14/2.39 inference(transitivity,[status(thm)],[11405, 4408])).
% 2.14/2.39 tff(11411,plain,
% 2.14/2.39 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11410])).
% 2.14/2.39 tff(11412,plain,
% 2.14/2.39 (~(elem!1 = z)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[74, 11411])).
% 2.14/2.39 tff(11413,plain,
% 2.14/2.39 (~b(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2456, 925, 1659, 11380])).
% 2.14/2.39 tff(11414,plain,
% 2.14/2.39 (r(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1759, 11413, 11412])).
% 2.14/2.39 tff(11415,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11366])).
% 2.14/2.39 tff(11416,plain,
% 2.14/2.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11373, 11415])).
% 2.14/2.39 tff(11417,plain,
% 2.14/2.39 ((elem!1 = s(s(z))) <=> (s(elem!1) = s(z))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11390, 8522])).
% 2.14/2.39 tff(11418,plain,
% 2.14/2.39 ((~(elem!1 = s(s(z)))) <=> (~(s(elem!1) = s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11417])).
% 2.14/2.39 tff(11419,plain,
% 2.14/2.39 (~(s(elem!1) = s(z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11395, 11418])).
% 2.14/2.39 tff(11420,plain,
% 2.14/2.39 (b(z, s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[935, 925, 445])).
% 2.14/2.39 tff(11421,plain,
% 2.14/2.39 (~b(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4299, 11420, 1659, 1658])).
% 2.14/2.39 tff(11422,plain,
% 2.14/2.39 (r(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[963, 11421])).
% 2.14/2.39 tff(11423,plain,
% 2.14/2.39 ((~(elem!1 = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11390])).
% 2.14/2.39 tff(11424,plain,
% 2.14/2.39 (~(s(elem!1) = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11395, 11423])).
% 2.14/2.39 tff(11425,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.39 tff(11426,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(11427,plain,
% 2.14/2.39 (((~b(s(elem!1), elem!1)) | (~b(z, 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(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(11428,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11427])).
% 2.14/2.39 tff(11429,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11428, 11426])).
% 2.14/2.39 tff(11430,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, 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)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(11431,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11430, 11429])).
% 2.14/2.39 tff(11432,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11431, 337, 925, 2520, 982, 597, 11425])).
% 2.14/2.39 tff(11433,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(11434,plain,
% 2.14/2.39 (~b(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11433, 2520, 925, 597, 11425])).
% 2.14/2.39 tff(11435,plain,
% 2.14/2.39 (r(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1015, 11434, 11396])).
% 2.14/2.39 tff(11436,plain,
% 2.14/2.39 (~r(s(elem!1), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1023, 11435, 274])).
% 2.14/2.39 tff(11437,plain,
% 2.14/2.39 (b(s(elem!1), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1262, 11436, 445])).
% 2.14/2.39 tff(11438,plain,
% 2.14/2.39 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[432])).
% 2.14/2.39 tff(11439,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[245])).
% 2.14/2.39 tff(11440,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11439, 11438])).
% 2.14/2.39 tff(11441,plain,
% 2.14/2.39 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2551, 2543, 352])).
% 2.14/2.39 tff(11442,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[363, 11441, 172])).
% 2.14/2.39 tff(11443,plain,
% 2.14/2.39 (~r(s(elem!1), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1023, 2543, 274])).
% 2.14/2.39 tff(11444,plain,
% 2.14/2.39 (b(s(elem!1), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1262, 11443, 230])).
% 2.14/2.39 tff(11445,plain,
% 2.14/2.39 (~r(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1032, 2543, 274])).
% 2.14/2.39 tff(11446,plain,
% 2.14/2.39 (b(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[395, 11445])).
% 2.14/2.39 tff(11447,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1927, 11446, 11444, 11442, 1925])).
% 2.14/2.39 tff(11448,plain,((~r(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(11449,plain,
% 2.14/2.39 (~b(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11448, 11435, 11416, 445, 352, 274])).
% 2.14/2.39 tff(11450,plain,
% 2.14/2.39 (r(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[146, 11449])).
% 2.14/2.39 tff(11451,plain,
% 2.14/2.39 (~r(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[291, 11450, 274])).
% 2.14/2.39 tff(11452,plain,
% 2.14/2.39 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1144, 11451, 445])).
% 2.14/2.39 tff(11453,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1150, 11452])).
% 2.14/2.39 tff(11454,plain,
% 2.14/2.39 (b(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[11453, 11440])).
% 2.14/2.39 tff(11455,plain,
% 2.14/2.39 (~r(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1032, 11435, 274])).
% 2.14/2.39 tff(11456,plain,
% 2.14/2.39 (b(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[395, 11455])).
% 2.14/2.39 tff(11457,plain,
% 2.14/2.39 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2551, 11435, 352])).
% 2.14/2.39 tff(11458,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[363, 11457, 11416])).
% 2.14/2.39 tff(11459,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2559, 337, 925, 11458, 11456, 2520, 11454, 11437])).
% 2.14/2.39 tff(11460,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(11461,plain,
% 2.14/2.39 (~b(s(elem!1), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11460, 925, 245, 11414, 352, 11409, 11387])).
% 2.14/2.39 tff(11462,plain,
% 2.14/2.39 (r(s(elem!1), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[270, 11461, 11424])).
% 2.14/2.39 tff(11463,plain,
% 2.14/2.39 (b(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1699, 11462, 11414, 11422, 11419, 11416])).
% 2.14/2.39 tff(11464,plain,
% 2.14/2.39 (~r(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[11448, 11463, 11416, 445, 352, 11414])).
% 2.14/2.39 tff(11465,plain,
% 2.14/2.39 (b(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1015, 11464, 11396])).
% 2.14/2.39 tff(11466,plain,
% 2.14/2.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[991, 189, 11462, 352])).
% 2.14/2.39 tff(11467,plain,
% 2.14/2.39 (b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[579, 11466, 11374])).
% 2.14/2.39 tff(11468,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(11469,plain,
% 2.14/2.39 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(11470,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[11469])).
% 2.14/2.39 tff(11471,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[11470, 11468])).
% 2.14/2.39 tff(11472,plain,
% 2.14/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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)))),
% 2.14/2.40 inference(quant_inst,[status(thm)],[])).
% 2.14/2.40 tff(11473,plain,
% 2.14/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[11472, 11471])).
% 2.14/2.40 tff(11474,plain,
% 2.14/2.40 ($false),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[11473, 337, 925, 11467, 11463, 11465, 11409, 11387])).
% 2.14/2.40 tff(11475,plain,((~b(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.40 tff(11476,plain,
% 2.14/2.40 (~b(z, elem!1)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[11475, 11403, 245, 1659, 1658])).
% 2.14/2.40 tff(11477,plain,
% 2.14/2.40 (r(z, elem!1)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[921, 11476, 11407])).
% 2.14/2.40 tff(11478,plain,
% 2.14/2.40 (~r(z, s(s(s(elem!1))))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[752, 189, 11477, 11403])).
% 2.14/2.40 tff(11479,plain,
% 2.14/2.40 (b(z, s(s(s(elem!1))))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[146, 11478])).
% 2.14/2.40 tff(11480,plain,
% 2.14/2.40 (~r(s(s(s(elem!1))), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[8710, 189, 11477, 11403])).
% 2.14/2.40 tff(11481,plain,
% 2.14/2.40 (b(s(s(s(elem!1))), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[406, 43, 133, 11480])).
% 2.14/2.40 tff(11482,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(11483,plain,
% 2.14/2.40 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(11484,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(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(X1, 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(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[11483])).
% 2.14/2.40 tff(11485,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(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(X1, 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(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.40 inference(transitivity,[status(thm)],[11484, 11482])).
% 2.14/2.40 tff(11486,plain,
% 2.14/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11487,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 2.24/2.40 tff(11488,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11487, 337, 1763, 1925, 3639, 597, 11425])).
% 2.24/2.40 tff(11489,plain,((~b(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)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(11490,plain,
% 2.24/2.40 (~b(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11489, 11479, 11481, 11409, 11387])).
% 2.24/2.40 tff(11491,plain,
% 2.24/2.40 (r(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1759, 11490, 11412])).
% 2.24/2.40 tff(11492,plain,
% 2.24/2.40 (~r(elem!1, s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11448, 11491, 11416, 445, 11403, 11479])).
% 2.24/2.40 tff(11493,plain,
% 2.24/2.40 (b(elem!1, s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1015, 11492, 11396])).
% 2.24/2.40 tff(11494,plain,
% 2.24/2.40 (~r(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[765, 11477, 11403, 11416])).
% 2.24/2.40 tff(11495,plain,
% 2.24/2.40 (b(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[270, 11494, 11424])).
% 2.24/2.40 tff(11496,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11497,plain,
% 2.24/2.40 (((~b(s(elem!1), elem!1)) | (~b(s(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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11498,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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(X1, 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), s(s(elem!1))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11497])).
% 2.24/2.40 tff(11499,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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(X1, 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), s(s(elem!1)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11498, 11496])).
% 2.24/2.40 tff(11500,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11501,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11500, 11499])).
% 2.24/2.40 tff(11502,plain,
% 2.24/2.40 (~b(s(elem!1), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11501, 337, 11495, 11493, 11387])).
% 2.24/2.40 tff(11503,plain,
% 2.24/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11502, 11378])).
% 2.24/2.40 tff(11504,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4267, 11503, 2008])).
% 2.24/2.40 tff(11505,plain,
% 2.24/2.40 (r(s(elem!1), s(s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11504, 11376])).
% 2.24/2.40 tff(11506,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11507,plain,
% 2.24/2.40 (((~b(s(s(s(elem!1))), z)) | (~b(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)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11508,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11507])).
% 2.24/2.40 tff(11509,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11508, 11506])).
% 2.24/2.40 tff(11510,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11511,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11510, 11509])).
% 2.24/2.40 tff(11512,plain,
% 2.24/2.40 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11511, 337, 11479, 11481, 11409])).
% 2.24/2.40 tff(11513,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11512, 437])).
% 2.24/2.40 tff(11514,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[524, 11513])).
% 2.24/2.40 tff(11515,plain,
% 2.24/2.40 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11514, 435])).
% 2.24/2.40 tff(11516,plain,
% 2.24/2.40 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[573, 189])).
% 2.24/2.40 tff(11517,plain,
% 2.24/2.40 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11516, 11515, 11505])).
% 2.24/2.40 tff(11518,plain,
% 2.24/2.40 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[579, 11517, 11374])).
% 2.24/2.40 tff(11519,plain,
% 2.24/2.40 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11520,plain,
% 2.24/2.40 (((~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(elem!1), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11521,plain,
% 2.24/2.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1), s(s(elem!1))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11520])).
% 2.24/2.40 tff(11522,plain,
% 2.24/2.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1), s(s(elem!1)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11521, 11519])).
% 2.24/2.40 tff(11523,plain,
% 2.24/2.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11524,plain,
% 2.24/2.40 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11523, 11522])).
% 2.24/2.40 tff(11525,plain,
% 2.24/2.40 ((~r(s(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))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11524, 189])).
% 2.24/2.40 tff(11526,plain,
% 2.24/2.40 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11525, 11515, 11505])).
% 2.24/2.40 tff(11527,plain,
% 2.24/2.40 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[363, 11526, 11416])).
% 2.24/2.40 tff(11528,plain,
% 2.24/2.40 (~b(z, s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[8015, 11527, 11479, 11518])).
% 2.24/2.40 tff(11529,plain,
% 2.24/2.40 (r(z, s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[395, 11528])).
% 2.24/2.40 tff(11530,plain,
% 2.24/2.40 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[430, 429])).
% 2.24/2.40 tff(11531,plain,
% 2.24/2.40 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.40 tff(11532,plain,
% 2.24/2.40 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.24/2.40 inference(symmetry,[status(thm)],[11531])).
% 2.24/2.40 tff(11533,plain,
% 2.24/2.40 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.40 tff(11534,plain,
% 2.24/2.40 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11533, 11532])).
% 2.24/2.40 tff(11535,plain,
% 2.24/2.40 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(z))), s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11534])).
% 2.24/2.40 tff(11536,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(elem!1))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11537,plain,
% 2.24/2.40 (((~b(s(elem!1), elem!1)) | (~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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11538,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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(s(elem!1)), s(elem!1)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11537])).
% 2.24/2.40 tff(11539,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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(X1, 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(s(elem!1)), s(elem!1))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11538, 11536])).
% 2.24/2.40 tff(11540,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11541,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11540, 11539])).
% 2.24/2.40 tff(11542,plain,
% 2.24/2.40 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11541, 337, 11495, 11493, 11387])).
% 2.24/2.40 tff(11543,plain,
% 2.24/2.40 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11542, 11535])).
% 2.24/2.40 tff(11544,plain,
% 2.24/2.40 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2853, 11543, 2009])).
% 2.24/2.40 tff(11545,plain,
% 2.24/2.40 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11544, 11530])).
% 2.24/2.40 tff(11546,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.40 inference(symmetry,[status(thm)],[595])).
% 2.24/2.40 tff(11547,plain,
% 2.24/2.40 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[592])).
% 2.24/2.40 tff(11548,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.24/2.40 tff(11549,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[653, 189, 11548, 615])).
% 2.24/2.40 tff(11550,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11549, 11547])).
% 2.24/2.40 tff(11551,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3252, 11550])).
% 2.24/2.40 tff(11552,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11551, 11546])).
% 2.24/2.40 tff(11553,plain,
% 2.24/2.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11554,plain,
% 2.24/2.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11555,plain,
% 2.24/2.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11554, 11553])).
% 2.24/2.40 tff(11556,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11555, 189, 1077, 11548])).
% 2.24/2.40 tff(11557,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[663, 11556])).
% 2.24/2.40 tff(11558,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11559,plain,
% 2.24/2.40 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11560,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[11559])).
% 2.24/2.40 tff(11561,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11560, 11558])).
% 2.24/2.40 tff(11562,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(11563,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11562, 11561])).
% 2.24/2.40 tff(11564,plain,
% 2.24/2.40 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11563, 337, 1925, 11557, 3639, 597])).
% 2.24/2.40 tff(11565,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11564, 11552])).
% 2.24/2.40 tff(11566,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(11567,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[11566, 245, 11479, 11481, 11409, 11545, 11529])).
% 2.24/2.40 tff(11568,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[649, 11567, 637])).
% 2.24/2.40 tff(11569,plain,
% 2.24/2.40 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4506, 337, 11527, 11495, 11493, 11568])).
% 2.24/2.40 tff(11570,plain,
% 2.24/2.40 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11569, 11364])).
% 2.24/2.40 tff(11571,plain,
% 2.24/2.40 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6726, 11570, 11360])).
% 2.24/2.40 tff(11572,plain,
% 2.24/2.40 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11571, 11349])).
% 2.24/2.40 tff(11573,plain,
% 2.24/2.40 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[11572, 11348])).
% 2.24/2.40 tff(11574,plain,
% 2.24/2.40 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.40 tff(11575,plain,
% 2.24/2.40 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[11574, 3256])).
% 2.24/2.41 tff(11576,plain,
% 2.24/2.41 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[11575, 6671])).
% 2.24/2.41 tff(11577,plain,
% 2.24/2.41 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11576])).
% 2.24/2.41 tff(11578,plain,
% 2.24/2.41 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[135, 11577])).
% 2.24/2.41 tff(11579,plain,
% 2.24/2.41 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11580,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(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(X1, 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(s(s(s(elem!1)))), s(elem!1)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11579])).
% 2.24/2.41 tff(11581,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(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(X1, 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(s(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11580, 6895])).
% 2.24/2.41 tff(11582,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11583,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11582, 11581])).
% 2.24/2.41 tff(11584,plain,
% 2.24/2.41 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11583, 337, 11495, 11493, 11568])).
% 2.24/2.41 tff(11585,plain,
% 2.24/2.41 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[714, 11584, 11578])).
% 2.24/2.41 tff(11586,plain,
% 2.24/2.41 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7690, 189, 11403, 11585])).
% 2.24/2.41 tff(11587,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11586, 11573])).
% 2.24/2.41 tff(11588,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11589,plain,
% 2.24/2.41 (~b(s(s(s(z))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11588, 11347, 1658, 11289])).
% 2.24/2.41 tff(11590,plain,
% 2.24/2.41 (r(s(s(s(z))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1498, 11589])).
% 2.24/2.41 tff(11591,plain,
% 2.24/2.41 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.41 tff(11592,plain,
% 2.24/2.41 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.24/2.41 inference(symmetry,[status(thm)],[11591])).
% 2.24/2.41 tff(11593,plain,
% 2.24/2.41 (r(s(s(elem!1)), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1474, 11592])).
% 2.24/2.41 tff(11594,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 2.24/2.41 tff(11595,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11594, 11593])).
% 2.24/2.41 tff(11596,plain,(r(s(s(elem!1)), z) | (~r(s(s(s(z))), z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11597,plain,
% 2.24/2.41 (r(s(s(elem!1)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11596, 11590, 11289])).
% 2.24/2.41 tff(11598,plain,
% 2.24/2.41 (r(z, s(z)) <=> r(z, elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.41 tff(11599,plain,
% 2.24/2.41 (r(z, elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[81, 11598])).
% 2.24/2.41 tff(11600,plain,
% 2.24/2.41 (~r(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[765, 11331, 11310, 11599])).
% 2.24/2.41 tff(11601,plain,
% 2.24/2.41 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.41 tff(11602,plain,
% 2.24/2.41 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11601])).
% 2.24/2.41 tff(11603,plain,
% 2.24/2.41 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11602])).
% 2.24/2.41 tff(11604,plain,
% 2.24/2.41 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 2.24/2.41 inference(bind,[status(th)],[])).
% 2.24/2.41 tff(11605,plain,
% 2.24/2.41 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.24/2.41 inference(quant_intro,[status(thm)],[11604])).
% 2.24/2.41 tff(11606,plain,
% 2.24/2.41 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11607,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 2.24/2.41 tff(11608,plain,
% 2.24/2.41 (![X: $i] : (~r(X, X))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11607, 11606])).
% 2.24/2.41 tff(11609,plain,(
% 2.24/2.41 ![X: $i] : (~r(X, X))),
% 2.24/2.41 inference(skolemize,[status(sab)],[11608])).
% 2.24/2.41 tff(11610,plain,
% 2.24/2.41 (![X: $i] : (~r(X, X))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11609, 11605])).
% 2.24/2.41 tff(11611,plain,
% 2.24/2.41 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11612,plain,
% 2.24/2.41 (~r(elem!1, elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11611, 11610])).
% 2.24/2.41 tff(11613,plain,
% 2.24/2.41 (~r(elem!1, s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11612, 11603])).
% 2.24/2.41 tff(11614,plain,
% 2.24/2.41 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.41 tff(11615,plain,
% 2.24/2.41 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11614])).
% 2.24/2.41 tff(11616,plain,
% 2.24/2.41 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11615])).
% 2.24/2.41 tff(11617,plain,
% 2.24/2.41 (~r(s(elem!1), s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11600, 11616])).
% 2.24/2.41 tff(11618,plain,
% 2.24/2.41 (~b(s(elem!1), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3763, 11617, 81, 11613, 11310, 11600, 1878])).
% 2.24/2.41 tff(11619,plain,
% 2.24/2.41 (r(s(elem!1), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1262, 11618, 11296])).
% 2.24/2.41 tff(11620,plain,
% 2.24/2.41 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10951, 11619, 11597])).
% 2.24/2.41 tff(11621,plain,
% 2.24/2.41 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11620, 11344])).
% 2.24/2.41 tff(11622,plain,
% 2.24/2.41 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2854, 11621])).
% 2.24/2.41 tff(11623,plain,
% 2.24/2.41 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11622, 11339])).
% 2.24/2.41 tff(11624,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11335])).
% 2.24/2.41 tff(11625,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(symmetry,[status(thm)],[11624])).
% 2.24/2.41 tff(11626,plain,
% 2.24/2.41 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.41 tff(11627,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1658, 11626])).
% 2.24/2.41 tff(11628,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11627, 11625])).
% 2.24/2.41 tff(11629,plain,
% 2.24/2.41 (b(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[270, 11600, 11333])).
% 2.24/2.41 tff(11630,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.24/2.41 tff(11631,plain,
% 2.24/2.41 (((~b(elem!1, s(elem!1))) | (~b(elem!1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11632,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, 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(X1, 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(s(elem!1)), s(elem!1)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11631])).
% 2.24/2.41 tff(11633,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, 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(X1, 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(s(elem!1)), s(elem!1))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11632, 11536])).
% 2.24/2.41 tff(11634,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, 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)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11635,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11634, 11633])).
% 2.24/2.41 tff(11636,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11635, 337, 2520, 982, 11425, 11630])).
% 2.24/2.41 tff(11637,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11638,plain,
% 2.24/2.41 (~b(elem!1, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11637, 11629, 11628, 11623])).
% 2.24/2.41 tff(11639,plain,
% 2.24/2.41 (r(elem!1, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1015, 11638, 11334])).
% 2.24/2.41 tff(11640,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2551, 11639, 11331])).
% 2.24/2.41 tff(11641,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[363, 11640, 11310])).
% 2.24/2.41 tff(11642,plain,
% 2.24/2.41 ((s(z) = z) <=> (elem!1 = z)),
% 2.24/2.41 inference(transitivity,[status(thm)],[11312, 4408])).
% 2.24/2.41 tff(11643,plain,
% 2.24/2.41 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11642])).
% 2.24/2.41 tff(11644,plain,
% 2.24/2.41 (~(elem!1 = z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[74, 11643])).
% 2.24/2.41 tff(11645,plain,
% 2.24/2.41 (~r(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11448, 11639, 11296, 11327, 11310, 11331])).
% 2.24/2.41 tff(11646,plain,
% 2.24/2.41 (b(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1759, 11645, 11644])).
% 2.24/2.41 tff(11647,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), z)) | (~b(z, 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(X1, 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(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11648,plain,
% 2.24/2.41 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~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(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11649,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~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(X1, 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(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11648])).
% 2.24/2.41 tff(11650,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~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(X1, 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(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11649, 11647])).
% 2.24/2.41 tff(11651,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(elem!1))) | (~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))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11652,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11651, 11650])).
% 2.24/2.41 tff(11653,plain,
% 2.24/2.41 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11652, 337, 11646, 11641, 11327, 11324])).
% 2.24/2.41 tff(11654,plain,
% 2.24/2.41 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11653, 11320])).
% 2.24/2.41 tff(11655,plain,
% 2.24/2.41 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.41 tff(11656,plain,
% 2.24/2.41 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11655])).
% 2.24/2.41 tff(11657,plain,
% 2.24/2.41 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11290])).
% 2.24/2.41 tff(11658,plain,
% 2.24/2.41 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11657])).
% 2.24/2.41 tff(11659,plain,
% 2.24/2.41 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11658, 11656])).
% 2.24/2.41 tff(11660,plain,
% 2.24/2.41 ((~b(elem!1, s(elem!1))) <=> (~b(s(z), s(s(z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11659])).
% 2.24/2.41 tff(11661,plain,
% 2.24/2.41 (~b(s(z), s(s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11638, 11660])).
% 2.24/2.41 tff(11662,plain,
% 2.24/2.41 (r(s(z), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8207, 11661])).
% 2.24/2.41 tff(11663,plain,
% 2.24/2.41 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11304, 9814])).
% 2.24/2.41 tff(11664,plain,
% 2.24/2.41 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11663])).
% 2.24/2.41 tff(11665,plain,
% 2.24/2.41 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11309, 11664])).
% 2.24/2.41 tff(11666,plain,
% 2.24/2.41 (~r(z, s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3378, 11662, 81])).
% 2.24/2.41 tff(11667,plain,
% 2.24/2.41 (~r(z, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1108, 11666, 11296])).
% 2.24/2.41 tff(11668,plain,
% 2.24/2.41 (b(z, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[395, 11667])).
% 2.24/2.41 tff(11669,plain,
% 2.24/2.41 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8015, 11668, 11327, 11641])).
% 2.24/2.41 tff(11670,plain,
% 2.24/2.41 (r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[579, 11669, 11665])).
% 2.24/2.41 tff(11671,plain,
% 2.24/2.41 (r(s(elem!1), s(s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1113, 3175])).
% 2.24/2.41 tff(11672,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.24/2.41 tff(11673,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11672, 11671])).
% 2.24/2.41 tff(11674,plain,((~r(s(elem!1), s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11675,plain,
% 2.24/2.41 (r(s(elem!1), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11674, 11670, 11296])).
% 2.24/2.41 tff(11676,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10135, 189, 1141, 3370])).
% 2.24/2.41 tff(11677,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11676, 3560])).
% 2.24/2.41 tff(11678,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11679,plain,
% 2.24/2.41 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11678, 11675, 11662, 11296])).
% 2.24/2.41 tff(11680,plain,
% 2.24/2.41 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1150, 11679])).
% 2.24/2.41 tff(11681,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11680, 11654])).
% 2.24/2.41 tff(11682,plain,(r(s(z), elem!1) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z)) | b(z, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11683,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11682, 69, 1658, 1878, 4381])).
% 2.24/2.41 tff(11684,plain,
% 2.24/2.41 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 2.24/2.41 inference(commutativity,[status(thm)],[])).
% 2.24/2.41 tff(11685,plain,
% 2.24/2.41 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11684])).
% 2.24/2.41 tff(11686,plain,
% 2.24/2.41 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11685])).
% 2.24/2.41 tff(11687,plain,
% 2.24/2.41 (~(z = s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[209, 11686])).
% 2.24/2.41 tff(11688,plain,
% 2.24/2.41 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.41 tff(11689,plain,
% 2.24/2.41 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.24/2.41 inference(symmetry,[status(thm)],[11688])).
% 2.24/2.41 tff(11690,plain,
% 2.24/2.41 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11689])).
% 2.24/2.41 tff(11691,plain,
% 2.24/2.41 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.41 tff(11692,plain,
% 2.24/2.41 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.41 tff(11693,plain,
% 2.24/2.41 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[11692, 11691])).
% 2.24/2.41 tff(11694,plain,
% 2.24/2.41 (r(z, s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3047, 147, 445])).
% 2.24/2.41 tff(11695,plain,
% 2.24/2.41 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1580, 11694, 173])).
% 2.24/2.41 tff(11696,plain,
% 2.24/2.41 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1150, 11695])).
% 2.24/2.41 tff(11697,plain,
% 2.24/2.41 (~b(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10521, 11696, 1658, 1231])).
% 2.24/2.41 tff(11698,plain,
% 2.24/2.41 (r(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2229, 11697])).
% 2.24/2.41 tff(11699,plain,
% 2.24/2.41 (r(s(elem!1), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11698, 11693])).
% 2.24/2.41 tff(11700,plain,
% 2.24/2.41 (r(s(z), z) <=> r(elem!1, z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.41 tff(11701,plain,
% 2.24/2.41 (r(elem!1, z) <=> r(s(z), z)),
% 2.24/2.41 inference(symmetry,[status(thm)],[11700])).
% 2.24/2.41 tff(11702,plain,
% 2.24/2.41 (r(s(z), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[274, 11701])).
% 2.24/2.41 tff(11703,plain,
% 2.24/2.41 ((elem!1 = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.41 tff(11704,plain,
% 2.24/2.41 ((elem!1 = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[11703, 975])).
% 2.24/2.41 tff(11705,plain,
% 2.24/2.41 ((elem!1 = s(s(z))) <=> (s(elem!1) = s(z))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11704, 8522])).
% 2.24/2.41 tff(11706,plain,
% 2.24/2.41 ((~(elem!1 = s(s(z)))) <=> (~(s(elem!1) = s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11705])).
% 2.24/2.41 tff(11707,plain,
% 2.24/2.41 (~(s(elem!1) = s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11395, 11706])).
% 2.24/2.41 tff(11708,plain,
% 2.24/2.41 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[432])).
% 2.24/2.41 tff(11709,plain,
% 2.24/2.41 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11708])).
% 2.24/2.41 tff(11710,plain,
% 2.24/2.41 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.41 tff(11711,plain,
% 2.24/2.41 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11710, 4627])).
% 2.24/2.41 tff(11712,plain,
% 2.24/2.41 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11711])).
% 2.24/2.41 tff(11713,plain,
% 2.24/2.41 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[2263, 11712])).
% 2.24/2.41 tff(11714,plain,
% 2.24/2.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11713, 11709])).
% 2.24/2.41 tff(11715,plain,
% 2.24/2.41 (~r(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1699, 274, 82, 11714, 11707, 273])).
% 2.24/2.41 tff(11716,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11715, 11702])).
% 2.24/2.41 tff(11717,plain,((~r(elem!1, z)) | (~(s(z) = elem!1)) | b(z, s(s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11718,plain,
% 2.24/2.41 (~r(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11717, 82, 245, 11699])).
% 2.24/2.41 tff(11719,plain,
% 2.24/2.41 (b(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1759, 11718, 11412])).
% 2.24/2.41 tff(11720,plain,
% 2.24/2.41 (b(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6686, 11719, 445])).
% 2.24/2.41 tff(11721,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11380, 11382])).
% 2.24/2.41 tff(11722,plain,
% 2.24/2.41 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11696, 11440])).
% 2.24/2.41 tff(11723,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.41 tff(11724,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[11723, 11397])).
% 2.24/2.41 tff(11725,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1231, 11724])).
% 2.24/2.41 tff(11726,plain,
% 2.24/2.41 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.41 inference(symmetry,[status(thm)],[534])).
% 2.24/2.41 tff(11727,plain,
% 2.24/2.41 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[2, 11726])).
% 2.24/2.41 tff(11728,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11729,plain,
% 2.24/2.41 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~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))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11730,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~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))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11729])).
% 2.24/2.41 tff(11731,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~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))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11730, 11728])).
% 2.24/2.41 tff(11732,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~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))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11733,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11732, 11731])).
% 2.24/2.41 tff(11734,plain,
% 2.24/2.41 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11733, 337, 1763, 326, 325, 11425])).
% 2.24/2.41 tff(11735,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11734, 11727])).
% 2.24/2.41 tff(11736,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(11737,plain,
% 2.24/2.41 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11736, 11719, 245, 11725, 11722, 11721])).
% 2.24/2.41 tff(11738,plain,
% 2.24/2.41 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[548, 11737])).
% 2.24/2.41 tff(11739,plain,
% 2.24/2.41 (~r(s(s(s(z))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5075, 11738, 11694])).
% 2.24/2.41 tff(11740,plain,
% 2.24/2.41 (b(s(s(s(z))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1498, 11739])).
% 2.24/2.41 tff(11741,plain,
% 2.24/2.41 (~b(z, s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10680, 11740, 1658, 11720])).
% 2.24/2.41 tff(11742,plain,
% 2.24/2.41 (~b(z, s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11741, 11690])).
% 2.24/2.41 tff(11743,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11738, 533])).
% 2.24/2.41 tff(11744,plain,
% 2.24/2.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11745,plain,
% 2.24/2.41 (((~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(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11746,plain,
% 2.24/2.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[11745])).
% 2.24/2.41 tff(11747,plain,
% 2.24/2.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[11746, 11744])).
% 2.24/2.41 tff(11748,plain,
% 2.24/2.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11749,plain,
% 2.24/2.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[11748, 11747])).
% 2.24/2.41 tff(11750,plain,
% 2.24/2.41 (~r(z, s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[11749, 189, 147, 11743])).
% 2.24/2.41 tff(11751,plain,
% 2.24/2.41 (((~![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))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(11752,plain,
% 2.24/2.41 ((~![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))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(11753,plain,
% 2.24/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11752, 11751])).
% 2.24/2.42 tff(11754,plain,
% 2.24/2.42 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11753, 43, 11750])).
% 2.24/2.42 tff(11755,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11754, 11742, 11687])).
% 2.24/2.42 tff(11756,plain,(b(z, s(s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(11757,plain,
% 2.24/2.42 (b(z, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11756, 11683, 1658, 11289, 81])).
% 2.24/2.42 tff(11758,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11292])).
% 2.24/2.42 tff(11759,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(transitivity,[status(thm)],[11345, 11758])).
% 2.24/2.42 tff(11760,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11683, 11759])).
% 2.24/2.42 tff(11761,plain,
% 2.24/2.42 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7881, 445])).
% 2.24/2.42 tff(11762,plain,
% 2.24/2.42 (b(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3403, 1925, 445])).
% 2.24/2.42 tff(11763,plain,
% 2.24/2.42 ((elem!1 = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11704, 4587])).
% 2.24/2.42 tff(11764,plain,
% 2.24/2.42 ((~(elem!1 = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11763])).
% 2.24/2.42 tff(11765,plain,
% 2.24/2.42 (~(elem!1 = s(elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11395, 11764])).
% 2.24/2.42 tff(11766,plain,
% 2.24/2.42 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.42 tff(11767,plain,
% 2.24/2.42 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11766])).
% 2.24/2.42 tff(11768,plain,
% 2.24/2.42 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11767])).
% 2.24/2.42 tff(11769,plain,
% 2.24/2.42 (~r(elem!1, s(z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11612, 11768])).
% 2.24/2.42 tff(11770,plain,
% 2.24/2.42 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.42 tff(11771,plain,
% 2.24/2.42 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11770])).
% 2.24/2.42 tff(11772,plain,
% 2.24/2.42 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(z)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11771])).
% 2.24/2.42 tff(11773,plain,
% 2.24/2.42 (~r(s(elem!1), s(z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[3062, 11772])).
% 2.24/2.42 tff(11774,plain,
% 2.24/2.42 (~b(s(elem!1), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3763, 11773, 11769, 173, 11714, 3062, 1878])).
% 2.24/2.42 tff(11775,plain,
% 2.24/2.42 (r(s(elem!1), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1262, 11774, 445])).
% 2.24/2.42 tff(11776,plain,
% 2.24/2.42 (~r(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1023, 11775, 274])).
% 2.24/2.42 tff(11777,plain,
% 2.24/2.42 (b(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1015, 11776, 11765])).
% 2.24/2.42 tff(11778,plain,
% 2.24/2.42 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11708, 9814])).
% 2.24/2.42 tff(11779,plain,
% 2.24/2.42 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11778])).
% 2.24/2.42 tff(11780,plain,
% 2.24/2.42 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11713, 11779])).
% 2.24/2.42 tff(11781,plain,
% 2.24/2.42 ((~(elem!1 = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11704])).
% 2.24/2.42 tff(11782,plain,
% 2.24/2.42 (~(s(elem!1) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11395, 11781])).
% 2.24/2.42 tff(11783,plain,
% 2.24/2.42 (b(s(elem!1), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[270, 3062, 11782])).
% 2.24/2.42 tff(11784,plain,
% 2.24/2.42 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[454])).
% 2.24/2.42 tff(11785,plain,
% 2.24/2.42 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = s(elem!1))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11784])).
% 2.24/2.42 tff(11786,plain,
% 2.24/2.42 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11785])).
% 2.24/2.42 tff(11787,plain,
% 2.24/2.42 (~(s(s(s(z))) = s(elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[2009, 11786])).
% 2.24/2.42 tff(11788,plain,
% 2.24/2.42 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[432])).
% 2.24/2.42 tff(11789,plain,
% 2.24/2.42 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11788, 6380])).
% 2.24/2.42 tff(11790,plain,
% 2.24/2.42 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11789])).
% 2.24/2.42 tff(11791,plain,
% 2.24/2.42 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[519, 11790])).
% 2.24/2.42 tff(11792,plain,
% 2.24/2.42 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5886, 11777, 11791, 11787, 326, 11783, 2454])).
% 2.24/2.42 tff(11793,plain,
% 2.24/2.42 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[579, 11792, 11780])).
% 2.24/2.42 tff(11794,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9739, 337, 326, 11783, 11793, 11777])).
% 2.24/2.42 tff(11795,plain,(r(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | r(s(z), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(11796,plain,
% 2.24/2.42 (r(s(elem!1), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11795, 274, 2454, 11725, 173, 1878, 245])).
% 2.24/2.42 tff(11797,plain,
% 2.24/2.42 (r(s(elem!1), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1874, 11796, 445])).
% 2.24/2.42 tff(11798,plain,
% 2.24/2.42 (~r(s(elem!1), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[374, 11796, 370])).
% 2.24/2.42 tff(11799,plain,
% 2.24/2.42 (b(s(elem!1), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1262, 11798, 445])).
% 2.24/2.42 tff(11800,plain,
% 2.24/2.42 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.42 tff(11801,plain,
% 2.24/2.42 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11800])).
% 2.24/2.42 tff(11802,plain,
% 2.24/2.42 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[283, 11801])).
% 2.24/2.42 tff(11803,plain,
% 2.24/2.42 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5433, 11802, 788])).
% 2.24/2.42 tff(11804,plain,
% 2.24/2.42 (~r(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9242, 283, 274])).
% 2.24/2.42 tff(11805,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[406, 43, 133, 11804])).
% 2.24/2.42 tff(11806,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11807,plain,
% 2.24/2.42 (((~b(s(s(s(elem!1))), elem!1)) | (~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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11808,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11807])).
% 2.24/2.42 tff(11809,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11808, 11806])).
% 2.24/2.42 tff(11810,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(11811,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11810, 11809])).
% 2.24/2.42 tff(11812,plain,
% 2.24/2.42 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11811, 337, 326, 1925, 599])).
% 2.24/2.42 tff(11813,plain,
% 2.24/2.42 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11812, 11805])).
% 2.24/2.42 tff(11814,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[579, 11813, 11803, 11780])).
% 2.24/2.42 tff(11815,plain,((~r(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), z)) | (~r(s(elem!1), s(z))) | (~(s(z) = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(11816,plain,
% 2.24/2.42 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11815, 11799, 1925, 11725, 11797, 245, 274])).
% 2.24/2.42 tff(11817,plain,
% 2.24/2.42 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1144, 11816, 445])).
% 2.24/2.42 tff(11818,plain,
% 2.24/2.42 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1150, 11817])).
% 2.24/2.42 tff(11819,plain,
% 2.24/2.42 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7953, 11818, 445, 11762, 1231, 274])).
% 2.24/2.42 tff(11820,plain,
% 2.24/2.42 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6726, 11819, 11761])).
% 2.24/2.42 tff(11821,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11820, 11349])).
% 2.24/2.42 tff(11822,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11821, 11348])).
% 2.24/2.42 tff(11823,plain,
% 2.24/2.42 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.42 tff(11824,plain,
% 2.24/2.42 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.24/2.42 inference(symmetry,[status(thm)],[11823])).
% 2.24/2.42 tff(11825,plain,
% 2.24/2.42 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11824])).
% 2.24/2.42 tff(11826,plain,
% 2.24/2.42 (~r(s(s(z)), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11798, 11825])).
% 2.24/2.42 tff(11827,plain,
% 2.24/2.42 (b(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2242, 11826])).
% 2.24/2.42 tff(11828,plain,
% 2.24/2.42 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (z = elem!1) | (~r(s(z), z)) | (~b(s(s(z)), z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1325, 2009])).
% 2.24/2.42 tff(11829,plain,
% 2.24/2.42 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11828, 11818, 445, 11702, 11796, 11407, 11827, 1231])).
% 2.24/2.42 tff(11830,plain,
% 2.24/2.42 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[548, 11829])).
% 2.24/2.42 tff(11831,plain,
% 2.24/2.42 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11830, 533])).
% 2.24/2.42 tff(11832,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11833,plain,
% 2.24/2.42 (((~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(s(s(elem!1)))), s(s(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(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11834,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11833])).
% 2.24/2.42 tff(11835,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11834, 11832])).
% 2.24/2.42 tff(11836,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(11837,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11836, 11835])).
% 2.24/2.42 tff(11838,plain,
% 2.24/2.42 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11837, 189, 11831])).
% 2.24/2.42 tff(11839,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11838, 11822])).
% 2.24/2.42 tff(11840,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11839, 11547])).
% 2.24/2.42 tff(11841,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3252, 11840])).
% 2.24/2.42 tff(11842,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11841, 11546])).
% 2.24/2.42 tff(11843,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.42 tff(11844,plain,
% 2.24/2.42 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11843])).
% 2.24/2.42 tff(11845,plain,
% 2.24/2.42 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.42 tff(11846,plain,
% 2.24/2.42 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11845])).
% 2.24/2.42 tff(11847,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11848,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(11849,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11848, 11847])).
% 2.24/2.42 tff(11850,plain,
% 2.24/2.42 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11849, 189, 11831])).
% 2.24/2.42 tff(11851,plain,
% 2.24/2.42 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11850, 11822])).
% 2.24/2.42 tff(11852,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11851, 11846])).
% 2.24/2.42 tff(11853,plain,
% 2.24/2.42 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1821, 11852])).
% 2.24/2.42 tff(11854,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11853, 11844])).
% 2.24/2.42 tff(11855,plain,
% 2.24/2.42 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11575])).
% 2.24/2.42 tff(11856,plain,
% 2.24/2.42 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[135, 11855])).
% 2.24/2.42 tff(11857,plain,
% 2.24/2.42 (~r(z, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1748, 11796, 370])).
% 2.24/2.42 tff(11858,plain,
% 2.24/2.42 (b(z, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[395, 11857])).
% 2.24/2.42 tff(11859,plain,
% 2.24/2.42 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[454, 7448])).
% 2.24/2.42 tff(11860,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[11859])).
% 2.24/2.42 tff(11861,plain,
% 2.24/2.42 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7461, 3277, 245, 273])).
% 2.24/2.42 tff(11862,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3299, 11861, 636])).
% 2.24/2.42 tff(11863,plain,
% 2.24/2.42 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11862, 11860])).
% 2.24/2.42 tff(11864,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3285, 3277, 274])).
% 2.24/2.42 tff(11865,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[663, 11864])).
% 2.24/2.42 tff(11866,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11867,plain,
% 2.24/2.42 (((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11868,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11867])).
% 2.24/2.42 tff(11869,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11868, 11866])).
% 2.24/2.42 tff(11870,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(11871,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11870, 11869])).
% 2.24/2.42 tff(11872,plain,
% 2.24/2.42 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11871, 337, 600, 599, 11865])).
% 2.24/2.42 tff(11873,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11872, 11863])).
% 2.24/2.42 tff(11874,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~(s(z) = elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(11875,plain,
% 2.24/2.42 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11874, 11858, 245, 274, 11796, 11799])).
% 2.24/2.42 tff(11876,plain,
% 2.24/2.42 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3274, 11875, 11856])).
% 2.24/2.42 tff(11877,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11878,plain,
% 2.24/2.42 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(11879,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(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(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[11878])).
% 2.24/2.42 tff(11880,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(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(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[11879, 11877])).
% 2.24/2.42 tff(11881,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(11882,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[11881, 11880])).
% 2.24/2.42 tff(11883,plain,
% 2.24/2.42 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11882, 337, 11876, 11383])).
% 2.24/2.42 tff(11884,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11883, 11854, 11842])).
% 2.24/2.42 tff(11885,plain,((~r(elem!1, z)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(11886,plain,
% 2.24/2.42 (~r(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[11885, 11683, 11289, 11757, 11316, 11627, 81, 1878])).
% 2.24/2.42 tff(11887,plain,
% 2.24/2.42 (b(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1759, 11886, 11644])).
% 2.24/2.42 tff(11888,plain,
% 2.24/2.42 (~b(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3647, 11887, 11760, 11757])).
% 2.24/2.43 tff(11889,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[406, 43, 133, 11888])).
% 2.24/2.43 tff(11890,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.43 tff(11891,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[11890])).
% 2.24/2.43 tff(11892,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[433])).
% 2.24/2.43 tff(11893,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11892, 11891])).
% 2.24/2.43 tff(11894,plain,
% 2.24/2.43 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11893])).
% 2.24/2.43 tff(11895,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11896,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11897,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11896, 11895])).
% 2.24/2.43 tff(11898,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11897, 189, 11775, 2177])).
% 2.24/2.43 tff(11899,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11898, 11894])).
% 2.24/2.43 tff(11900,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11901,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11902,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11901, 11900])).
% 2.24/2.43 tff(11903,plain,
% 2.24/2.43 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11902, 189, 11775, 2177])).
% 2.24/2.43 tff(11904,plain,
% 2.24/2.43 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[579, 11903, 11780])).
% 2.24/2.43 tff(11905,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1133, 11904, 445])).
% 2.24/2.43 tff(11906,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[363, 11898, 11714])).
% 2.24/2.43 tff(11907,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11908,plain,
% 2.24/2.43 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11909,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11908])).
% 2.24/2.43 tff(11910,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11909, 11907])).
% 2.24/2.43 tff(11911,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11912,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11911, 11910])).
% 2.24/2.43 tff(11913,plain,
% 2.24/2.43 ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(elem!1))) | (~b(elem!1, z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11912, 337])).
% 2.24/2.43 tff(11914,plain,
% 2.24/2.43 (~b(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11913, 11906, 11725, 1763, 11783, 11904])).
% 2.24/2.43 tff(11915,plain,
% 2.24/2.43 (r(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[395, 11914])).
% 2.24/2.43 tff(11916,plain,
% 2.24/2.43 (r(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1108, 11915, 445])).
% 2.24/2.43 tff(11917,plain,
% 2.24/2.43 (~r(s(z), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3378, 11916, 173])).
% 2.24/2.43 tff(11918,plain,
% 2.24/2.43 (b(s(z), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[8207, 11917])).
% 2.24/2.43 tff(11919,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(s(s(s(z)))), s(z))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11920,plain,
% 2.24/2.43 (((~b(s(s(s(s(z)))), 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(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)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11921,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~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(s(s(s(z)))), s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11920])).
% 2.24/2.43 tff(11922,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~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(s(s(s(z)))), s(z))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11921, 11919])).
% 2.24/2.43 tff(11923,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11924,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11923, 11922])).
% 2.24/2.43 tff(11925,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11924, 337, 1231, 1396, 7465, 3477])).
% 2.24/2.43 tff(11926,plain,((~b(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)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(11927,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11926, 11918, 1231, 11905])).
% 2.24/2.43 tff(11928,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9040, 11927])).
% 2.24/2.43 tff(11929,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11928, 11899])).
% 2.24/2.43 tff(11930,plain,(r(s(elem!1), elem!1) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(11931,plain,
% 2.24/2.43 (r(s(elem!1), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11930, 11683, 11289, 81, 11887, 11889, 1878])).
% 2.24/2.43 tff(11932,plain,
% 2.24/2.43 (~r(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1748, 11931, 11316])).
% 2.24/2.43 tff(11933,plain,
% 2.24/2.43 (b(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[395, 11932])).
% 2.24/2.43 tff(11934,plain,
% 2.24/2.43 (~r(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[374, 11931, 11316])).
% 2.24/2.43 tff(11935,plain,
% 2.24/2.43 (b(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1262, 11934, 11296])).
% 2.24/2.43 tff(11936,plain,
% 2.24/2.43 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1927, 11935, 11757, 11933])).
% 2.24/2.43 tff(11937,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[363, 11936, 11310])).
% 2.24/2.43 tff(11938,plain,
% 2.24/2.43 ((elem!1 = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11298, 4587])).
% 2.24/2.43 tff(11939,plain,
% 2.24/2.43 ((~(elem!1 = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11938])).
% 2.24/2.43 tff(11940,plain,
% 2.24/2.43 (~(elem!1 = s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11302, 11939])).
% 2.24/2.43 tff(11941,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11942,plain,
% 2.24/2.43 (((~b(s(elem!1), z)) | (~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(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11943,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11942])).
% 2.24/2.43 tff(11944,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11943, 11941])).
% 2.24/2.43 tff(11945,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~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))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11946,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11945, 11944])).
% 2.24/2.43 tff(11947,plain,
% 2.24/2.43 (~b(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11946, 337, 11887, 11933, 11935])).
% 2.24/2.43 tff(11948,plain,
% 2.24/2.43 (r(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1015, 11947, 11940])).
% 2.24/2.43 tff(11949,plain,
% 2.24/2.43 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[8021, 11948, 11937])).
% 2.24/2.43 tff(11950,plain,
% 2.24/2.43 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1144, 11949, 11296])).
% 2.24/2.43 tff(11951,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1150, 11950])).
% 2.24/2.43 tff(11952,plain,
% 2.24/2.43 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11951, 11295])).
% 2.24/2.43 tff(11953,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11954,plain,
% 2.24/2.43 (((~b(elem!1, s(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~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))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(11955,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[11954])).
% 2.24/2.43 tff(11956,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11955, 11953])).
% 2.24/2.43 tff(11957,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(11958,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11957, 11956])).
% 2.24/2.43 tff(11959,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11958, 337, 11887, 11760, 11757, 11952])).
% 2.24/2.43 tff(11960,plain,(b(z, s(z)) | r(s(z), elem!1) | (~b(s(s(s(z))), s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(11961,plain,
% 2.24/2.43 (b(z, s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11960, 1878, 1658, 4381])).
% 2.24/2.43 tff(11962,plain,
% 2.24/2.43 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.43 tff(11963,plain,
% 2.24/2.43 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.24/2.43 inference(symmetry,[status(thm)],[11962])).
% 2.24/2.43 tff(11964,plain,
% 2.24/2.43 (b(s(elem!1), s(z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[2520, 11963])).
% 2.24/2.43 tff(11965,plain,
% 2.24/2.43 (b(s(z), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6686, 1763, 445])).
% 2.24/2.43 tff(11966,plain,
% 2.24/2.43 (~b(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[8824, 11965, 1301, 1544])).
% 2.24/2.43 tff(11967,plain,
% 2.24/2.43 (r(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1262, 11966, 445])).
% 2.24/2.43 tff(11968,plain,
% 2.24/2.43 (b(z, elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6585, 1301, 445])).
% 2.24/2.43 tff(11969,plain,
% 2.24/2.43 (~b(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2456, 1763, 11380, 11968])).
% 2.24/2.43 tff(11970,plain,
% 2.24/2.43 (r(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1498, 11969])).
% 2.24/2.43 tff(11971,plain,
% 2.24/2.43 (r(s(s(elem!1)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11596, 11970, 245])).
% 2.24/2.43 tff(11972,plain,
% 2.24/2.43 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10951, 11971, 11967])).
% 2.24/2.43 tff(11973,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[431])).
% 2.24/2.43 tff(11974,plain,
% 2.24/2.43 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(symmetry,[status(thm)],[11973])).
% 2.24/2.43 tff(11975,plain,
% 2.24/2.43 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.43 tff(11976,plain,
% 2.24/2.43 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11975, 11974])).
% 2.24/2.43 tff(11977,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10871, 11976])).
% 2.24/2.43 tff(11978,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.24/2.43 tff(11979,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11978, 11977])).
% 2.24/2.43 tff(11980,plain,((~r(s(s(s(z))), s(s(z)))) | r(s(s(elem!1)), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(11981,plain,
% 2.24/2.43 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11980, 11972, 245])).
% 2.24/2.43 tff(11982,plain,
% 2.24/2.43 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2854, 11981])).
% 2.24/2.43 tff(11983,plain,
% 2.24/2.43 (b(s(s(s(z))), s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11982, 11531])).
% 2.24/2.43 tff(11984,plain,
% 2.24/2.43 (~b(s(s(s(z))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5010, 11965, 1658, 1301, 1544])).
% 2.24/2.43 tff(11985,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11984, 11983])).
% 2.24/2.43 tff(11986,plain,((~b(elem!1, z)) | (~(s(z) = elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(11987,plain,
% 2.24/2.43 (~b(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11986, 11964, 1301, 245, 1658])).
% 2.24/2.43 tff(11988,plain,
% 2.24/2.43 (r(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1759, 11987, 11412])).
% 2.24/2.43 tff(11989,plain,
% 2.24/2.43 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(symmetry,[status(thm)],[11533])).
% 2.24/2.43 tff(11990,plain,
% 2.24/2.43 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(transitivity,[status(thm)],[11531, 11989])).
% 2.24/2.43 tff(11991,plain,
% 2.24/2.43 (~b(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11475, 352, 1658, 245, 925])).
% 2.24/2.43 tff(11992,plain,
% 2.24/2.43 (r(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1498, 11991])).
% 2.24/2.43 tff(11993,plain,
% 2.24/2.43 (r(s(s(elem!1)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11596, 11992, 245])).
% 2.24/2.43 tff(11994,plain,
% 2.24/2.43 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1144, 739, 445])).
% 2.24/2.43 tff(11995,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1150, 11994])).
% 2.24/2.43 tff(11996,plain,
% 2.24/2.43 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[11995, 11440])).
% 2.24/2.43 tff(11997,plain,
% 2.24/2.43 (~r(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2530, 11996, 2520, 11714, 274, 11765, 215])).
% 2.24/2.43 tff(11998,plain,
% 2.24/2.43 (b(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[395, 11997])).
% 2.24/2.43 tff(11999,plain,
% 2.24/2.43 (~b(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2540, 11998, 925, 2520])).
% 2.24/2.43 tff(12000,plain,
% 2.24/2.43 (r(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1015, 11999, 11765])).
% 2.24/2.43 tff(12001,plain,
% 2.24/2.43 (~r(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1023, 12000, 274])).
% 2.24/2.43 tff(12002,plain,
% 2.24/2.43 (b(s(elem!1), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1262, 12001, 445])).
% 2.24/2.43 tff(12003,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[432])).
% 2.24/2.43 tff(12004,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.43 tff(12005,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(transitivity,[status(thm)],[12004, 12003])).
% 2.24/2.43 tff(12006,plain,
% 2.24/2.43 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[245])).
% 2.24/2.43 tff(12007,plain,
% 2.24/2.43 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.24/2.43 inference(symmetry,[status(thm)],[12006])).
% 2.24/2.43 tff(12008,plain,
% 2.24/2.43 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.43 tff(12009,plain,
% 2.24/2.43 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.24/2.43 inference(symmetry,[status(thm)],[12008])).
% 2.24/2.43 tff(12010,plain,
% 2.24/2.43 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 2.24/2.43 inference(transitivity,[status(thm)],[12009, 12007])).
% 2.24/2.43 tff(12011,plain,
% 2.24/2.43 (b(s(s(z)), s(z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[2520, 12010])).
% 2.24/2.43 tff(12012,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10521, 11995, 1658, 12011])).
% 2.24/2.43 tff(12013,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[851, 12012])).
% 2.24/2.43 tff(12014,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[12013, 12005])).
% 2.24/2.43 tff(12015,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2551, 12000, 12014])).
% 2.24/2.43 tff(12016,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[363, 12015, 11714])).
% 2.24/2.43 tff(12017,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2559, 337, 925, 12016, 11998, 2520, 11996, 12002])).
% 2.24/2.43 tff(12018,plain,((~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(12019,plain,
% 2.24/2.43 (~r(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[12018, 2520, 925, 274, 245, 1658])).
% 2.24/2.43 tff(12020,plain,
% 2.24/2.43 (b(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[146, 12019])).
% 2.24/2.43 tff(12021,plain,
% 2.24/2.43 (~r(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[11448, 352, 445, 274, 11714, 12020])).
% 2.24/2.43 tff(12022,plain,
% 2.24/2.43 (b(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1015, 12021, 11765])).
% 2.24/2.43 tff(12023,plain,
% 2.24/2.43 (~b(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2540, 12022, 925, 2520])).
% 2.24/2.43 tff(12024,plain,
% 2.24/2.43 (r(z, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[395, 12023])).
% 2.24/2.43 tff(12025,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(12026,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12027,plain,
% 2.24/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12026, 12025])).
% 2.24/2.44 tff(12028,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12027, 189, 1077, 615, 10946])).
% 2.24/2.44 tff(12029,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(12030,plain,
% 2.24/2.44 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12029, 12024, 11993])).
% 2.24/2.44 tff(12031,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[11980, 12030, 245])).
% 2.24/2.44 tff(12032,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2854, 12031])).
% 2.24/2.44 tff(12033,plain,
% 2.24/2.44 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12032, 11990])).
% 2.24/2.44 tff(12034,plain,
% 2.24/2.44 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[11637, 12022, 11721, 2520])).
% 2.24/2.44 tff(12035,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12034, 12033])).
% 2.24/2.44 tff(12036,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(12037,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12036, 2520, 245, 11968, 1658, 11988])).
% 2.24/2.44 tff(12038,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[350, 12037, 11402])).
% 2.24/2.44 tff(12039,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(symmetry,[status(thm)],[11723])).
% 2.24/2.44 tff(12040,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[11397])).
% 2.24/2.44 tff(12041,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12040, 12039])).
% 2.24/2.44 tff(12042,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12038, 12041])).
% 2.24/2.44 tff(12043,plain,
% 2.24/2.44 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10521, 12042, 1658, 12011])).
% 2.24/2.44 tff(12044,plain,
% 2.24/2.44 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1150, 12043])).
% 2.24/2.44 tff(12045,plain,
% 2.24/2.44 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1144, 12044, 445])).
% 2.24/2.44 tff(12046,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9242, 12045, 11988])).
% 2.24/2.44 tff(12047,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[406, 43, 133, 12046])).
% 2.24/2.44 tff(12048,plain,
% 2.24/2.44 (r(s(z), z)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[11988, 11701])).
% 2.24/2.44 tff(12049,plain,
% 2.24/2.44 (~r(s(elem!1), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4044, 12042, 11968, 2520, 12048, 11713, 1301, 11707])).
% 2.24/2.44 tff(12050,plain,
% 2.24/2.44 (b(s(elem!1), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1262, 12049, 445])).
% 2.24/2.44 tff(12051,plain,
% 2.24/2.44 (~r(z, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12018, 2520, 11968, 11988, 245, 1658])).
% 2.24/2.44 tff(12052,plain,
% 2.24/2.44 (b(z, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[146, 12051])).
% 2.24/2.44 tff(12053,plain,
% 2.24/2.44 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[11811, 337, 12038, 12052, 12050, 12047])).
% 2.24/2.44 tff(12054,plain,
% 2.24/2.44 (r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[579, 12053, 11780])).
% 2.24/2.44 tff(12055,plain,
% 2.24/2.44 (~b(elem!1, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5886, 12054, 11791, 11787, 12038, 2520, 11380])).
% 2.24/2.44 tff(12056,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12057,plain,
% 2.24/2.44 (((~b(s(s(s(elem!1))), z)) | (~b(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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12058,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12057])).
% 2.24/2.44 tff(12059,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12058, 12056])).
% 2.24/2.44 tff(12060,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12061,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12060, 12059])).
% 2.24/2.44 tff(12062,plain,
% 2.24/2.44 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12061, 337, 12052, 12050, 12047])).
% 2.24/2.44 tff(12063,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[363, 12062, 11714])).
% 2.24/2.44 tff(12064,plain,
% 2.24/2.44 (~r(elem!1, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[8021, 12063, 12045])).
% 2.24/2.44 tff(12065,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1015, 12064, 12055, 11765])).
% 2.24/2.44 tff(12066,plain,((~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(12067,plain,
% 2.24/2.44 (~b(s(elem!1), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12066, 11961, 1658, 11289])).
% 2.24/2.44 tff(12068,plain,
% 2.24/2.44 (r(s(elem!1), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[270, 12067, 11303])).
% 2.24/2.44 tff(12069,plain,
% 2.24/2.44 (b(z, elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6585, 11961, 11296])).
% 2.24/2.44 tff(12070,plain,
% 2.24/2.44 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[11349, 11348])).
% 2.24/2.44 tff(12071,plain,
% 2.24/2.44 (~b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2456, 1763, 2454, 925])).
% 2.24/2.44 tff(12072,plain,
% 2.24/2.44 (r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1498, 12071])).
% 2.24/2.44 tff(12073,plain,
% 2.24/2.44 (r(z, s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3047, 215, 445])).
% 2.24/2.44 tff(12074,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5075, 12073, 1474])).
% 2.24/2.44 tff(12075,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[548, 12074])).
% 2.24/2.44 tff(12076,plain,
% 2.24/2.44 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12075, 11726])).
% 2.24/2.44 tff(12077,plain,
% 2.24/2.44 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[617])).
% 2.24/2.44 tff(12078,plain,
% 2.24/2.44 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.24/2.44 inference(symmetry,[status(thm)],[12077])).
% 2.24/2.44 tff(12079,plain,
% 2.24/2.44 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[11349])).
% 2.24/2.44 tff(12080,plain,
% 2.24/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[674, 12079])).
% 2.24/2.44 tff(12081,plain,
% 2.24/2.44 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12080])).
% 2.24/2.44 tff(12082,plain,
% 2.24/2.44 (r(s(s(elem!1)), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[11596, 1474, 245])).
% 2.24/2.44 tff(12083,plain,
% 2.24/2.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[991, 189, 273, 352])).
% 2.24/2.44 tff(12084,plain,
% 2.24/2.44 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[579, 12083, 11780])).
% 2.24/2.44 tff(12085,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[356, 189, 273, 352])).
% 2.24/2.44 tff(12086,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[363, 12085, 11714])).
% 2.24/2.44 tff(12087,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12088,plain,
% 2.24/2.44 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(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))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12089,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12088])).
% 2.24/2.44 tff(12090,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12089, 12087])).
% 2.24/2.44 tff(12091,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12092,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12091, 12090])).
% 2.24/2.44 tff(12093,plain,
% 2.24/2.44 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12092, 337, 12086, 12084])).
% 2.24/2.44 tff(12094,plain,
% 2.24/2.44 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12093, 12076])).
% 2.24/2.44 tff(12095,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12094, 11535])).
% 2.24/2.44 tff(12096,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2854, 12095])).
% 2.24/2.44 tff(12097,plain,
% 2.24/2.44 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[11980, 12096, 245])).
% 2.24/2.44 tff(12098,plain,
% 2.24/2.44 (~r(s(elem!1), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10951, 12097, 12082])).
% 2.24/2.44 tff(12099,plain,
% 2.24/2.44 (b(s(elem!1), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1262, 12098, 445])).
% 2.24/2.44 tff(12100,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12101,plain,
% 2.24/2.44 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12102,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(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(X1, 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), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12101])).
% 2.24/2.44 tff(12103,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(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(X1, 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), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12102, 12100])).
% 2.24/2.44 tff(12104,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12105,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12104, 12103])).
% 2.24/2.44 tff(12106,plain,
% 2.24/2.44 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12105, 337, 1763, 12086, 12099, 11425, 12076])).
% 2.24/2.44 tff(12107,plain,
% 2.24/2.44 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[295, 43, 625, 12106])).
% 2.24/2.44 tff(12108,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.44 tff(12109,plain,
% 2.24/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12110,plain,
% 2.24/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12111,plain,
% 2.24/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12110, 12109])).
% 2.24/2.44 tff(12112,plain,
% 2.24/2.44 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12111, 189, 215])).
% 2.24/2.44 tff(12113,plain,
% 2.24/2.44 (~r(s(s(s(s(elem!1)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12112, 12108])).
% 2.24/2.44 tff(12114,plain,
% 2.24/2.44 (b(s(s(s(s(elem!1)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[663, 12113])).
% 2.24/2.44 tff(12115,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 2.24/2.44 tff(12116,plain,
% 2.24/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12117,plain,
% 2.24/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12118,plain,
% 2.24/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12117, 12116])).
% 2.24/2.44 tff(12119,plain,
% 2.24/2.44 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12118, 189, 283])).
% 2.24/2.44 tff(12120,plain,
% 2.24/2.44 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12119, 12108])).
% 2.24/2.44 tff(12121,plain,
% 2.24/2.44 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[714, 12120, 12115])).
% 2.24/2.44 tff(12122,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4455, 337, 925, 1763, 12121, 12114])).
% 2.24/2.44 tff(12123,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(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(12124,plain,
% 2.24/2.44 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12123, 12107, 1763, 11578, 215, 925])).
% 2.24/2.44 tff(12125,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12124, 12081])).
% 2.24/2.44 tff(12126,plain,
% 2.24/2.44 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6726, 12125, 11761])).
% 2.24/2.44 tff(12127,plain,
% 2.24/2.44 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12126, 11361])).
% 2.24/2.44 tff(12128,plain,
% 2.24/2.44 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12127, 673])).
% 2.24/2.44 tff(12129,plain,
% 2.24/2.44 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7448, 454])).
% 2.24/2.44 tff(12130,plain,
% 2.24/2.44 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12129, 7355])).
% 2.24/2.44 tff(12131,plain,
% 2.24/2.44 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.24/2.44 inference(symmetry,[status(thm)],[12130])).
% 2.24/2.44 tff(12132,plain,
% 2.24/2.44 ((~(s(s(z)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12131])).
% 2.24/2.44 tff(12133,plain,
% 2.24/2.44 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10141, 12132])).
% 2.24/2.44 tff(12134,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12135,plain,
% 2.24/2.44 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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(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(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12136,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(elem!1)))), s(elem!1)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12135])).
% 2.24/2.44 tff(12137,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12136, 12134])).
% 2.24/2.44 tff(12138,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12139,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)))), s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[12138, 12137])).
% 2.24/2.44 tff(12140,plain,
% 2.24/2.44 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12139, 337, 12086, 12084])).
% 2.24/2.44 tff(12141,plain,
% 2.24/2.44 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12140, 12128])).
% 2.24/2.44 tff(12142,plain,
% 2.24/2.44 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[649, 12141, 12133])).
% 2.24/2.44 tff(12143,plain,
% 2.24/2.44 (~r(z, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[12029, 12097, 12082])).
% 2.24/2.44 tff(12144,plain,
% 2.24/2.44 (b(z, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[395, 12143])).
% 2.24/2.44 tff(12145,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12146,plain,
% 2.24/2.44 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(12147,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[12146])).
% 2.24/2.44 tff(12148,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[12147, 12145])).
% 2.24/2.44 tff(12149,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(12150,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12149, 12148])).
% 2.24/2.45 tff(12151,plain,
% 2.24/2.45 (~b(elem!1, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12150, 337, 1763, 12144, 12084, 12099])).
% 2.24/2.45 tff(12152,plain,
% 2.24/2.45 (r(elem!1, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1015, 12151, 11765])).
% 2.24/2.45 tff(12153,plain,
% 2.24/2.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12154,plain,
% 2.24/2.45 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12155,plain,
% 2.24/2.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12154])).
% 2.24/2.45 tff(12156,plain,
% 2.24/2.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12155, 12153])).
% 2.24/2.45 tff(12157,plain,
% 2.24/2.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(12158,plain,
% 2.24/2.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12157, 12156])).
% 2.24/2.45 tff(12159,plain,
% 2.24/2.45 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12158, 189, 12152, 12142])).
% 2.24/2.45 tff(12160,plain,
% 2.24/2.45 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3274, 12159, 11856])).
% 2.24/2.45 tff(12161,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12162,plain,
% 2.24/2.45 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12163,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12162])).
% 2.24/2.45 tff(12164,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12163, 12161])).
% 2.24/2.45 tff(12165,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(12166,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12165, 12164])).
% 2.24/2.45 tff(12167,plain,
% 2.24/2.45 ((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12166, 337, 1763, 12144, 12084])).
% 2.24/2.45 tff(12168,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12167, 12160, 12128])).
% 2.24/2.45 tff(12169,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[663, 12168])).
% 2.24/2.45 tff(12170,plain,
% 2.24/2.45 (r(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12169, 12078])).
% 2.24/2.45 tff(12171,plain,
% 2.24/2.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[617])).
% 2.24/2.45 tff(12172,plain,
% 2.24/2.45 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[12171])).
% 2.24/2.45 tff(12173,plain,
% 2.24/2.45 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12172, 6663])).
% 2.24/2.45 tff(12174,plain,
% 2.24/2.45 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12173])).
% 2.24/2.45 tff(12175,plain,
% 2.24/2.45 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[116, 12174])).
% 2.24/2.45 tff(12176,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[432])).
% 2.24/2.45 tff(12177,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 2.24/2.45 inference(symmetry,[status(thm)],[12176])).
% 2.24/2.45 tff(12178,plain,
% 2.24/2.45 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12177])).
% 2.24/2.45 tff(12179,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12180,plain,
% 2.24/2.45 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12181,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12180])).
% 2.24/2.45 tff(12182,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12181, 12179])).
% 2.24/2.45 tff(12183,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(12184,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12183, 12182])).
% 2.24/2.45 tff(12185,plain,
% 2.24/2.45 (~b(s(s(s(elem!1))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12184, 337, 12086, 12144, 12084])).
% 2.24/2.45 tff(12186,plain,
% 2.24/2.45 (~b(s(s(s(s(z)))), z)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12185, 12178])).
% 2.24/2.45 tff(12187,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1792, 12186])).
% 2.24/2.45 tff(12188,plain,
% 2.24/2.45 (~r(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7566, 12187, 11761, 12175, 1474, 12075])).
% 2.24/2.45 tff(12189,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12188, 12170])).
% 2.24/2.45 tff(12190,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(12191,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12190, 215, 1763, 245, 925, 11425, 1474, 273])).
% 2.24/2.45 tff(12192,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[350, 12191, 11402])).
% 2.24/2.45 tff(12193,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12194,plain,
% 2.24/2.45 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(s(elem!1))), 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(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12195,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12194])).
% 2.24/2.45 tff(12196,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12195, 12193])).
% 2.24/2.45 tff(12197,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(12198,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12197, 12196])).
% 2.24/2.45 tff(12199,plain,
% 2.24/2.45 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12198, 337, 925, 1763, 12192, 11425])).
% 2.24/2.45 tff(12200,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12199, 12076])).
% 2.24/2.45 tff(12201,plain,((~r(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(12202,plain,
% 2.24/2.45 (~r(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12201, 1763, 925, 245, 11383, 12072, 273])).
% 2.24/2.45 tff(12203,plain,
% 2.24/2.45 (b(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[146, 12202])).
% 2.24/2.45 tff(12204,plain,
% 2.24/2.45 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7655, 12203, 925, 1763])).
% 2.24/2.45 tff(12205,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[350, 12204, 11402])).
% 2.24/2.45 tff(12206,plain,
% 2.24/2.45 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[991, 189, 273, 12205])).
% 2.24/2.45 tff(12207,plain,
% 2.24/2.45 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[579, 12206, 11780])).
% 2.24/2.45 tff(12208,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[358, 12205, 273])).
% 2.24/2.45 tff(12209,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[363, 12208, 11714])).
% 2.24/2.45 tff(12210,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.45 tff(12211,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(z, 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(X1, 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)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12212,plain,
% 2.24/2.45 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12213,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(X1, 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)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[12212])).
% 2.24/2.45 tff(12214,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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(X1, 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)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12213, 12211])).
% 2.24/2.45 tff(12215,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(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)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(12216,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12215, 12214])).
% 2.24/2.45 tff(12217,plain,
% 2.24/2.45 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12216, 337, 365, 638, 1925])).
% 2.24/2.45 tff(12218,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12217, 12210])).
% 2.24/2.45 tff(12219,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[663, 12218])).
% 2.24/2.45 tff(12220,plain,
% 2.24/2.45 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12139, 337, 365, 638])).
% 2.24/2.45 tff(12221,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12220, 12210])).
% 2.24/2.45 tff(12222,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[649, 12221, 3949])).
% 2.24/2.45 tff(12223,plain,
% 2.24/2.45 (~b(z, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8015, 638, 1925, 365])).
% 2.24/2.45 tff(12224,plain,
% 2.24/2.45 (r(z, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[395, 12223])).
% 2.24/2.45 tff(12225,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[11555, 189, 12224, 12222, 12219])).
% 2.24/2.45 tff(12226,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (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(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(12227,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12226, 12209, 12133, 12207, 12203])).
% 2.24/2.45 tff(12228,plain,
% 2.24/2.45 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12227, 11364])).
% 2.24/2.45 tff(12229,plain,
% 2.24/2.45 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6726, 12228, 11761])).
% 2.24/2.45 tff(12230,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12229, 12070])).
% 2.24/2.45 tff(12231,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[429])).
% 2.24/2.45 tff(12232,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[12231])).
% 2.24/2.45 tff(12233,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[433])).
% 2.24/2.45 tff(12234,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[12233, 12232])).
% 2.24/2.45 tff(12235,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[12209, 12234])).
% 2.24/2.45 tff(12236,plain,
% 2.24/2.45 (b(z, s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3403, 12203, 445])).
% 2.24/2.45 tff(12237,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1133, 12207, 445])).
% 2.24/2.45 tff(12238,plain,
% 2.24/2.45 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10844, 12237, 12236, 11965, 12235])).
% 2.24/2.45 tff(12239,plain,
% 2.24/2.45 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1150, 12238])).
% 2.24/2.45 tff(12240,plain,
% 2.24/2.45 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1144, 12239, 445])).
% 2.24/2.45 tff(12241,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[12118, 189, 12240, 12230])).
% 2.24/2.45 tff(12242,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[714, 12241, 11578])).
% 2.24/2.45 tff(12243,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(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(X1, 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)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12244,plain,
% 2.24/2.45 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~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, z)) | (~b(z, elem!1)) | (~b(s(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)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(12245,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~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(X1, 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)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12244])).
% 2.24/2.46 tff(12246,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~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(X1, 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)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12245, 12243])).
% 2.24/2.46 tff(12247,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~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)))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12248,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12247, 12246])).
% 2.24/2.46 tff(12249,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12248, 337, 925, 1763, 12242, 11383])).
% 2.24/2.46 tff(12250,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12249, 596])).
% 2.24/2.46 tff(12251,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3252, 12250])).
% 2.24/2.46 tff(12252,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12251, 593])).
% 2.24/2.46 tff(12253,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12254,plain,
% 2.24/2.46 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12255,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), 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(X1, 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(z, s(s(elem!1))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12254])).
% 2.24/2.46 tff(12256,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), 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(X1, 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(z, s(s(elem!1)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12255, 12253])).
% 2.24/2.46 tff(12257,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12258,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12257, 12256])).
% 2.24/2.46 tff(12259,plain,
% 2.24/2.46 (~b(z, s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12258, 337, 925, 1763, 11383])).
% 2.24/2.46 tff(12260,plain,
% 2.24/2.46 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11753, 43, 12259])).
% 2.24/2.46 tff(12261,plain,
% 2.24/2.46 (r(z, s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12260, 11687])).
% 2.24/2.46 tff(12262,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4455, 337, 925, 1763, 12242])).
% 2.24/2.46 tff(12263,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[663, 12262])).
% 2.24/2.46 tff(12264,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12265,plain,
% 2.24/2.46 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12266,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12265])).
% 2.24/2.46 tff(12267,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12266, 12264])).
% 2.24/2.46 tff(12268,plain,
% 2.24/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12269,plain,
% 2.24/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12268, 12267])).
% 2.24/2.46 tff(12270,plain,
% 2.24/2.46 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12269, 189, 12263, 12261])).
% 2.24/2.46 tff(12271,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12270, 12252])).
% 2.24/2.46 tff(12272,plain,((~b(elem!1, z)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(12273,plain,
% 2.24/2.46 (~b(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12272, 11289, 12069, 12068, 11627])).
% 2.24/2.46 tff(12274,plain,
% 2.24/2.46 (r(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1759, 12273, 11644])).
% 2.24/2.46 tff(12275,plain,
% 2.24/2.46 (~r(s(elem!1), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5224, 12274, 12068])).
% 2.24/2.46 tff(12276,plain,
% 2.24/2.46 (b(s(elem!1), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1262, 12275, 11296])).
% 2.24/2.46 tff(12277,plain,
% 2.24/2.46 (b(z, s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11717, 12274, 11289, 12068])).
% 2.24/2.46 tff(12278,plain,
% 2.24/2.46 (r(s(elem!1), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1874, 12068, 11296])).
% 2.24/2.46 tff(12279,plain,
% 2.24/2.46 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[11289])).
% 2.24/2.46 tff(12280,plain,
% 2.24/2.46 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.46 inference(transitivity,[status(thm)],[12279, 277])).
% 2.24/2.46 tff(12281,plain,
% 2.24/2.46 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12280])).
% 2.24/2.46 tff(12282,plain,
% 2.24/2.46 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[211, 12281])).
% 2.24/2.46 tff(12283,plain,
% 2.24/2.46 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[991, 189, 273, 4419])).
% 2.24/2.46 tff(12284,plain,
% 2.24/2.46 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[358, 4419, 273])).
% 2.24/2.46 tff(12285,plain,
% 2.24/2.46 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[363, 12284, 172])).
% 2.24/2.46 tff(12286,plain,
% 2.24/2.46 (~r(elem!1, s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11448, 4419, 230, 274, 172, 1925])).
% 2.24/2.46 tff(12287,plain,
% 2.24/2.46 (b(elem!1, s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1015, 12286, 1008])).
% 2.24/2.46 tff(12288,plain,
% 2.24/2.46 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1006, 12287, 273, 276, 983, 984, 12285])).
% 2.24/2.46 tff(12289,plain,
% 2.24/2.46 (~r(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9242, 12288, 274])).
% 2.24/2.46 tff(12290,plain,
% 2.24/2.46 (b(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[406, 43, 133, 12289])).
% 2.24/2.46 tff(12291,plain,
% 2.24/2.46 (~r(s(elem!1), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5224, 274, 273])).
% 2.24/2.46 tff(12292,plain,
% 2.24/2.46 (b(s(elem!1), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1262, 12291, 230])).
% 2.24/2.46 tff(12293,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12294,plain,
% 2.24/2.46 (((~b(s(s(s(elem!1))), s(elem!1))) | (~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(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12295,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12294])).
% 2.24/2.46 tff(12296,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12295, 12293])).
% 2.24/2.46 tff(12297,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(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))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12298,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 2.24/2.46 tff(12299,plain,
% 2.24/2.46 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12298, 337, 12285, 1925, 12292, 12290])).
% 2.24/2.46 tff(12300,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[579, 12299, 12283, 983])).
% 2.24/2.46 tff(12301,plain,(b(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(12302,plain,
% 2.24/2.46 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12301, 11665, 12277, 12068, 12274, 12282, 11940, 11310, 11296])).
% 2.24/2.46 tff(12303,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11815, 12302, 12278, 12277, 12274, 11289, 12276])).
% 2.24/2.46 tff(12304,plain,
% 2.24/2.46 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1144, 12303, 11296])).
% 2.24/2.46 tff(12305,plain,
% 2.24/2.46 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1150, 12304])).
% 2.24/2.46 tff(12306,plain,
% 2.24/2.46 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12305, 11295])).
% 2.24/2.46 tff(12307,plain,
% 2.24/2.46 (((~b(elem!1, s(s(s(elem!1))))) | (~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(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))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12308,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12307])).
% 2.24/2.46 tff(12309,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12308, 943])).
% 2.24/2.46 tff(12310,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12311,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12310, 12309])).
% 2.24/2.46 tff(12312,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12311, 337, 12069, 12302, 12277, 12306])).
% 2.24/2.46 tff(12313,plain,(r(s(z), elem!1) | (~b(s(s(s(z))), s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(12314,plain,
% 2.24/2.46 (b(s(z), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12313, 11288, 11273])).
% 2.24/2.46 tff(12315,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12314, 11285])).
% 2.24/2.46 tff(12316,plain,((~(elem!1 = s(z))) | b(s(z), s(z)) | (elem!1 = z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(12317,plain,
% 2.24/2.46 (~(elem!1 = s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12316, 3768, 11280, 6683])).
% 2.24/2.46 tff(12318,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12319,plain,
% 2.24/2.46 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(12320,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[12319])).
% 2.24/2.46 tff(12321,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[12320, 12318])).
% 2.24/2.46 tff(12322,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(12323,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[12322, 12321])).
% 2.24/2.46 tff(12324,plain,
% 2.24/2.46 (~b(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[12323, 337, 1301, 1658, 10691])).
% 2.24/2.46 tff(12325,plain,
% 2.24/2.46 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[199, 43, 12324])).
% 2.24/2.47 tff(12326,plain,
% 2.24/2.47 (r(z, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12325, 179])).
% 2.24/2.47 tff(12327,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12328,plain,
% 2.24/2.47 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), 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)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12329,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12328])).
% 2.24/2.47 tff(12330,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12329, 12327])).
% 2.24/2.47 tff(12331,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12332,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12331, 12330])).
% 2.24/2.47 tff(12333,plain,
% 2.24/2.47 (~b(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12332, 337, 1301, 1658, 3357, 10691])).
% 2.24/2.47 tff(12334,plain,
% 2.24/2.47 (r(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2242, 12333])).
% 2.24/2.47 tff(12335,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4275, 189, 10707, 12334, 12326])).
% 2.24/2.47 tff(12336,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12337,plain,
% 2.24/2.47 (~b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12336, 1301, 10691, 1658])).
% 2.24/2.47 tff(12338,plain,
% 2.24/2.47 (r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2229, 12337])).
% 2.24/2.47 tff(12339,plain,
% 2.24/2.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12340,plain,
% 2.24/2.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12341,plain,
% 2.24/2.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12340, 12339])).
% 2.24/2.47 tff(12342,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12341, 189, 275, 2245, 2244])).
% 2.24/2.47 tff(12343,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12344,plain,
% 2.24/2.47 (~r(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12343, 12338, 275])).
% 2.24/2.47 tff(12345,plain,
% 2.24/2.47 (b(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2242, 12344])).
% 2.24/2.47 tff(12346,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10440, 189, 811, 12338])).
% 2.24/2.47 tff(12347,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9040, 12346])).
% 2.24/2.47 tff(12348,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12349,plain,
% 2.24/2.47 (((~b(s(s(s(z))), s(z))) | (~b(z, 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))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12350,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, 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(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12349])).
% 2.24/2.47 tff(12351,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, 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(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12350, 12348])).
% 2.24/2.47 tff(12352,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, 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)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12353,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12352, 12351])).
% 2.24/2.47 tff(12354,plain,
% 2.24/2.47 (~b(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12353, 337, 1301, 1658, 10691])).
% 2.24/2.47 tff(12355,plain,
% 2.24/2.47 (r(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1498, 12354])).
% 2.24/2.47 tff(12356,plain,
% 2.24/2.47 (~r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5075, 12355, 1339])).
% 2.24/2.47 tff(12357,plain,
% 2.24/2.47 (b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1786, 12356])).
% 2.24/2.47 tff(12358,plain,
% 2.24/2.47 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1198, 189, 811, 12338])).
% 2.24/2.47 tff(12359,plain,
% 2.24/2.47 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2268, 12358])).
% 2.24/2.47 tff(12360,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12361,plain,
% 2.24/2.47 (((~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(s(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12362,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), z))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12361])).
% 2.24/2.47 tff(12363,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)), z)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12362, 12360])).
% 2.24/2.47 tff(12364,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12365,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12364, 12363])).
% 2.24/2.47 tff(12366,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12365, 337, 12359, 12357, 12347, 12345])).
% 2.24/2.47 tff(12367,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12368,plain,
% 2.24/2.47 (~b(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12367, 8520, 8866, 11272, 11273, 1339])).
% 2.24/2.47 tff(12369,plain,
% 2.24/2.47 (r(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[80, 12368])).
% 2.24/2.47 tff(12370,plain,
% 2.24/2.47 (~b(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12367, 811, 275, 11272, 1658, 1339])).
% 2.24/2.47 tff(12371,plain,
% 2.24/2.47 (r(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[80, 12370])).
% 2.24/2.47 tff(12372,plain,
% 2.24/2.47 (~r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1580, 12371, 11269])).
% 2.24/2.47 tff(12373,plain,
% 2.24/2.47 (b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1786, 12372])).
% 2.24/2.47 tff(12374,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2023, 12371, 811])).
% 2.24/2.47 tff(12375,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1792, 12374])).
% 2.24/2.47 tff(12376,plain,
% 2.24/2.47 (b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1759, 8867, 3768])).
% 2.24/2.47 tff(12377,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1908, 12376, 12375, 12373])).
% 2.24/2.47 tff(12378,plain,
% 2.24/2.47 (s(s(s(s(z)))) = elem!1),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[857, 8869, 12377])).
% 2.24/2.47 tff(12379,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8251, 12378, 1339])).
% 2.24/2.47 tff(12380,plain,
% 2.24/2.47 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[801, 12378, 247])).
% 2.24/2.47 tff(12381,plain,
% 2.24/2.47 (~r(z, elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[785, 4406, 12371])).
% 2.24/2.47 tff(12382,plain,
% 2.24/2.47 (b(z, elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[921, 12381, 65])).
% 2.24/2.47 tff(12383,plain,
% 2.24/2.47 (~(s(s(s(z))) = s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2510, 12378, 5308])).
% 2.24/2.47 tff(12384,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12385,plain,
% 2.24/2.47 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12386,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12385])).
% 2.24/2.47 tff(12387,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12386, 12384])).
% 2.24/2.47 tff(12388,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12389,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12388, 12387])).
% 2.24/2.47 tff(12390,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12389, 337, 5209, 1658, 10691])).
% 2.24/2.47 tff(12391,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4678, 43, 4643, 12390, 2484])).
% 2.24/2.47 tff(12392,plain,((~r(s(elem!1), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12393,plain,
% 2.24/2.47 (~r(s(elem!1), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12392, 12383, 1658, 11272, 5308, 4406, 12379])).
% 2.24/2.47 tff(12394,plain,
% 2.24/2.47 (~b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5643, 12378, 5641])).
% 2.24/2.47 tff(12395,plain,
% 2.24/2.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[170, 12378, 5308])).
% 2.24/2.47 tff(12396,plain,
% 2.24/2.47 (~(s(elem!1) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[264, 12395])).
% 2.24/2.47 tff(12397,plain,
% 2.24/2.47 (b(s(elem!1), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[270, 12393, 12396])).
% 2.24/2.47 tff(12398,plain,
% 2.24/2.47 (~b(z, s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2717, 12397, 12382, 12376])).
% 2.24/2.47 tff(12399,plain,
% 2.24/2.47 (r(z, s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[395, 12398])).
% 2.24/2.47 tff(12400,plain,
% 2.24/2.47 (b(z, s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5052, 12399, 4370, 247, 12381, 12394, 12393, 12376, 65])).
% 2.24/2.47 tff(12401,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7655, 12400, 12376, 12382])).
% 2.24/2.47 tff(12402,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[350, 12401, 12380])).
% 2.24/2.47 tff(12403,plain,
% 2.24/2.47 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2468, 189, 12402, 12379])).
% 2.24/2.47 tff(12404,plain,
% 2.24/2.47 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2473, 43, 5725, 12403])).
% 2.24/2.47 tff(12405,plain,
% 2.24/2.47 (~r(s(s(s(elem!1))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2153, 12402, 4406])).
% 2.24/2.47 tff(12406,plain,
% 2.24/2.47 (b(s(s(s(elem!1))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8966, 12405])).
% 2.24/2.47 tff(12407,plain,
% 2.24/2.47 (r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12313, 12394, 1658])).
% 2.24/2.47 tff(12408,plain,
% 2.24/2.47 (~r(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2164, 189, 12402, 12407])).
% 2.24/2.47 tff(12409,plain,
% 2.24/2.47 (b(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1970, 12408])).
% 2.24/2.47 tff(12410,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12411,plain,
% 2.24/2.47 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12412,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12411])).
% 2.24/2.47 tff(12413,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12412, 12410])).
% 2.24/2.47 tff(12414,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12415,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12414, 12413])).
% 2.24/2.47 tff(12416,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12415, 337, 12409, 12406, 11272, 12404])).
% 2.24/2.47 tff(12417,plain,((elem!1 = s(z)) | b(elem!1, s(z)) | (z = elem!1) | (~b(s(s(s(z))), s(z))) | b(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), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12418,plain,
% 2.24/2.47 (b(elem!1, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12417, 12317, 65, 11273, 5641, 1339, 8520, 8866])).
% 2.24/2.47 tff(12419,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12420,plain,
% 2.24/2.47 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12421,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[12420])).
% 2.24/2.47 tff(12422,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[12421, 12419])).
% 2.24/2.47 tff(12423,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(12424,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12423, 12422])).
% 2.24/2.47 tff(12425,plain,
% 2.24/2.47 (~b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12424, 337, 12418, 11273, 11272])).
% 2.24/2.47 tff(12426,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[327, 8637])).
% 2.24/2.47 tff(12427,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8519, 12426])).
% 2.24/2.47 tff(12428,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(s(z)))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12429,plain,
% 2.24/2.47 (~(s(s(s(s(z)))) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12428, 12418, 8519])).
% 2.24/2.47 tff(12430,plain,
% 2.24/2.47 (~r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1580, 12369, 11269])).
% 2.24/2.47 tff(12431,plain,
% 2.24/2.47 (b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1786, 12430])).
% 2.24/2.47 tff(12432,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2023, 12369, 8520])).
% 2.24/2.47 tff(12433,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1792, 12432])).
% 2.24/2.47 tff(12434,plain,
% 2.24/2.47 (~b(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12367, 811, 275, 3690, 1658, 1339])).
% 2.24/2.47 tff(12435,plain,
% 2.24/2.47 (r(z, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[80, 12434])).
% 2.24/2.47 tff(12436,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2023, 12435, 811])).
% 2.24/2.47 tff(12437,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1792, 12436])).
% 2.24/2.47 tff(12438,plain,
% 2.24/2.47 (~r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1580, 12435, 1141])).
% 2.24/2.47 tff(12439,plain,
% 2.24/2.47 (b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1786, 12438])).
% 2.24/2.47 tff(12440,plain,
% 2.24/2.47 (~r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2896, 1735, 275])).
% 2.24/2.47 tff(12441,plain,
% 2.24/2.47 (b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1759, 12440, 3768])).
% 2.24/2.47 tff(12442,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2992, 9612, 9182, 12441, 1592])).
% 2.24/2.47 tff(12443,plain,((~r(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (z = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12444,plain,
% 2.24/2.47 (~r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12443, 853, 12439, 65, 1141, 275])).
% 2.24/2.47 tff(12445,plain,
% 2.24/2.47 (b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12313, 12444, 1658])).
% 2.24/2.47 tff(12446,plain,
% 2.24/2.47 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10444, 2245, 811, 173])).
% 2.24/2.47 tff(12447,plain,
% 2.24/2.47 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2268, 12446])).
% 2.24/2.47 tff(12448,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1198, 189, 811, 12447, 2245])).
% 2.24/2.47 tff(12449,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(12450,plain,
% 2.24/2.47 (~r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12449, 811, 12435])).
% 2.24/2.47 tff(12451,plain,
% 2.24/2.47 (b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2229, 12450])).
% 2.24/2.47 tff(12452,plain,
% 2.24/2.47 (~b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[12424, 337, 327, 1658, 3690])).
% 2.24/2.47 tff(12453,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12454,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~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)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12455,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12454])).
% 2.24/2.48 tff(12456,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[12455, 12453])).
% 2.24/2.48 tff(12457,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(12458,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12457, 12456])).
% 2.24/2.48 tff(12459,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12458, 337, 327, 791, 1658, 3357])).
% 2.24/2.48 tff(12460,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4268, 12459])).
% 2.24/2.48 tff(12461,plain,
% 2.24/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12462,plain,
% 2.24/2.48 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12463,plain,
% 2.24/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12462])).
% 2.24/2.48 tff(12464,plain,
% 2.24/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[12463, 12461])).
% 2.24/2.48 tff(12465,plain,
% 2.24/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(12466,plain,
% 2.24/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12465, 12464])).
% 2.24/2.48 tff(12467,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12466, 189, 12460, 9918, 2465])).
% 2.24/2.48 tff(12468,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12469,plain,
% 2.24/2.48 (~r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12468, 156, 3357, 327, 791, 1658])).
% 2.24/2.48 tff(12470,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2463, 4932, 12469, 2460])).
% 2.24/2.48 tff(12471,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(z))), elem!1) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12472,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12471, 12452, 12451, 327, 12445, 1658, 247, 5308])).
% 2.24/2.48 tff(12473,plain,
% 2.24/2.48 (~(s(elem!1) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[264, 12472])).
% 2.24/2.48 tff(12474,plain,
% 2.24/2.48 (~(elem!1 = s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[980, 12473])).
% 2.24/2.48 tff(12475,plain,
% 2.24/2.48 (~r(z, s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2578, 274, 12435, 5308, 327, 12474, 12445])).
% 2.24/2.48 tff(12476,plain,
% 2.24/2.48 (b(z, s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[395, 12475])).
% 2.24/2.48 tff(12477,plain,
% 2.24/2.48 (b(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1970, 307])).
% 2.24/2.48 tff(12478,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3960, 12477, 272, 274, 247, 275])).
% 2.24/2.48 tff(12479,plain,
% 2.24/2.48 (~r(s(elem!1), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1754, 172, 173, 5308, 247, 274, 82])).
% 2.24/2.48 tff(12480,plain,
% 2.24/2.48 (b(s(elem!1), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[270, 12479, 265])).
% 2.24/2.48 tff(12481,plain,
% 2.24/2.48 (~b(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2563, 12480, 1711, 82, 274, 172])).
% 2.24/2.48 tff(12482,plain,
% 2.24/2.48 (r(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[921, 12481, 65])).
% 2.24/2.48 tff(12483,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7228, 12482, 147])).
% 2.24/2.48 tff(12484,plain,
% 2.24/2.48 (s(s(s(elem!1))) = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[350, 12483, 12478])).
% 2.24/2.48 tff(12485,plain,
% 2.24/2.48 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12484])).
% 2.24/2.48 tff(12486,plain,
% 2.24/2.48 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[12485])).
% 2.24/2.48 tff(12487,plain,
% 2.24/2.48 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12486])).
% 2.24/2.48 tff(12488,plain,
% 2.24/2.48 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.48 inference(symmetry,[status(thm)],[12487])).
% 2.24/2.48 tff(12489,plain,
% 2.24/2.48 ((~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12488])).
% 2.24/2.48 tff(12490,plain,
% 2.24/2.48 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1466, 12484, 5308])).
% 2.24/2.48 tff(12491,plain,
% 2.24/2.48 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12490, 12489])).
% 2.24/2.48 tff(12492,plain,
% 2.24/2.48 (~(s(s(s(z))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7671, 12484, 5725])).
% 2.24/2.48 tff(12493,plain,
% 2.24/2.48 (r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2463, 12492, 2460])).
% 2.24/2.48 tff(12494,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8151, 12493, 1339])).
% 2.24/2.48 tff(12495,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[857, 12494, 853])).
% 2.24/2.48 tff(12496,plain,
% 2.24/2.48 (s(s(s(s(z)))) = s(elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6992, 12495, 1711, 247, 12480, 5308, 275, 274, 12482])).
% 2.24/2.48 tff(12497,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12496, 12491])).
% 2.24/2.48 tff(12498,plain,((s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(z))), elem!1) | (z = elem!1) | b(z, s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12499,plain,
% 2.24/2.48 (b(z, s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12498, 274, 275, 12472, 853, 1339, 12452, 65, 247, 12435])).
% 2.24/2.48 tff(12500,plain,
% 2.24/2.48 (~r(elem!1, s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1709, 274, 12435])).
% 2.24/2.48 tff(12501,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7903, 6583, 12499])).
% 2.24/2.48 tff(12502,plain,
% 2.24/2.48 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1470])).
% 2.24/2.48 tff(12503,plain,
% 2.24/2.48 (r(s(z), s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[1141, 12502])).
% 2.24/2.48 tff(12504,plain,
% 2.24/2.48 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1470])).
% 2.24/2.48 tff(12505,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1469])).
% 2.24/2.48 tff(12506,plain,
% 2.24/2.48 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[1339, 12505])).
% 2.24/2.48 tff(12507,plain,
% 2.24/2.48 (r(elem!1, s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12506, 12504])).
% 2.24/2.48 tff(12508,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1470])).
% 2.24/2.48 tff(12509,plain,
% 2.24/2.48 (b(s(elem!1), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[1591, 12508])).
% 2.24/2.48 tff(12510,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1927, 12509, 1925, 600])).
% 2.24/2.48 tff(12511,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[363, 12510, 172])).
% 2.24/2.48 tff(12512,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2551, 12511, 12507])).
% 2.24/2.48 tff(12513,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[350, 12512, 276])).
% 2.24/2.48 tff(12514,plain,
% 2.24/2.48 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3960, 12513, 272, 274, 247, 275])).
% 2.24/2.48 tff(12515,plain,
% 2.24/2.48 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1970, 12514])).
% 2.24/2.48 tff(12516,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8317, 189, 12511, 12515, 12503])).
% 2.24/2.48 tff(12517,plain,((~(s(s(s(z))) = elem!1)) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~r(s(z), z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12518,plain,
% 2.24/2.48 (~(s(s(s(z))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12517, 12501, 247, 275, 274, 12472, 12499, 12476, 12437, 1141, 1339])).
% 2.24/2.48 tff(12519,plain,
% 2.24/2.48 (r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2463, 12518, 12452])).
% 2.24/2.48 tff(12520,plain,
% 2.24/2.48 (s(s(z)) = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12468, 12519, 12451, 327, 12445, 1658])).
% 2.24/2.48 tff(12521,plain,
% 2.24/2.48 (s(s(s(z))) = s(elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12520])).
% 2.24/2.48 tff(12522,plain,
% 2.24/2.48 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12521])).
% 2.24/2.48 tff(12523,plain,
% 2.24/2.48 (~b(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1493, 275, 1481, 1474, 274, 327])).
% 2.24/2.48 tff(12524,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[727, 12523, 6976, 2754])).
% 2.24/2.48 tff(12525,plain,((~r(s(z), z)) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12526,plain,
% 2.24/2.48 (~r(s(s(s(z))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12525, 12518, 275, 8707, 274, 272, 327])).
% 2.24/2.48 tff(12527,plain,
% 2.24/2.48 (b(s(s(s(z))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1498, 12526])).
% 2.24/2.48 tff(12528,plain,
% 2.24/2.48 (b(s(elem!1), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12527, 12522])).
% 2.24/2.48 tff(12529,plain,
% 2.24/2.48 (s(elem!1) = s(s(s(z)))),
% 2.24/2.48 inference(symmetry,[status(thm)],[12521])).
% 2.24/2.48 tff(12530,plain,
% 2.24/2.48 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12529])).
% 2.24/2.48 tff(12531,plain,
% 2.24/2.48 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.48 inference(symmetry,[status(thm)],[12530])).
% 2.24/2.48 tff(12532,plain,
% 2.24/2.48 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12531])).
% 2.24/2.48 tff(12533,plain,
% 2.24/2.48 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[519, 12532])).
% 2.24/2.48 tff(12534,plain,
% 2.24/2.48 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12529])).
% 2.24/2.48 tff(12535,plain,
% 2.24/2.48 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[12534])).
% 2.24/2.48 tff(12536,plain,
% 2.24/2.48 (r(s(elem!1), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12519, 12535])).
% 2.24/2.48 tff(12537,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[765, 12536, 12472, 8707])).
% 2.24/2.48 tff(12538,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1949, 12537, 12536, 12435, 5308, 12444, 811, 12472, 275, 12476, 3768, 12533, 12528, 12500, 853])).
% 2.24/2.48 tff(12539,plain,(b(z, elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12540,plain,
% 2.24/2.48 (b(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12539, 274, 275, 853, 327, 1658, 811, 247, 1141, 1339, 65])).
% 2.24/2.48 tff(12541,plain,
% 2.24/2.48 (s(s(z)) = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12468, 2465, 3357, 327, 791, 1658])).
% 2.24/2.48 tff(12542,plain,
% 2.24/2.48 (s(s(s(z))) = s(elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12541])).
% 2.24/2.48 tff(12543,plain,
% 2.24/2.48 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12542])).
% 2.24/2.48 tff(12544,plain,
% 2.24/2.48 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[12543])).
% 2.24/2.48 tff(12545,plain,
% 2.24/2.48 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12544])).
% 2.24/2.48 tff(12546,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[12545])).
% 2.24/2.48 tff(12547,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8151, 2465, 1339])).
% 2.24/2.48 tff(12548,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[857, 12547, 853])).
% 2.24/2.48 tff(12549,plain,
% 2.24/2.48 (b(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12548, 12546])).
% 2.24/2.48 tff(12550,plain,
% 2.24/2.48 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12542])).
% 2.24/2.48 tff(12551,plain,
% 2.24/2.48 (b(s(z), s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10691, 12550])).
% 2.24/2.48 tff(12552,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12543])).
% 2.24/2.48 tff(12553,plain,
% 2.24/2.48 (b(s(s(elem!1)), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[1591, 12552])).
% 2.24/2.48 tff(12554,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12555,plain,
% 2.24/2.48 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12556,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12555])).
% 2.24/2.48 tff(12557,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[12556, 12554])).
% 2.24/2.48 tff(12558,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(12559,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12558, 12557])).
% 2.24/2.48 tff(12560,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12559, 337, 925, 327, 600, 12553, 12551, 12549])).
% 2.24/2.48 tff(12561,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12562,plain,
% 2.24/2.48 (~r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12561, 12540, 327, 12476, 12437, 3690, 853, 12451, 12445, 1658, 1339])).
% 2.24/2.48 tff(12563,plain,
% 2.24/2.48 (s(s(s(z))) = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2463, 12562, 12452])).
% 2.24/2.48 tff(12564,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7671, 12563, 5725])).
% 2.24/2.48 tff(12565,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12517, 12564, 12563, 247, 275, 274, 12472, 12499, 12476, 12437, 1141, 1339])).
% 2.24/2.48 tff(12566,plain,((~r(elem!1, z)) | (elem!1 = s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12567,plain,
% 2.24/2.48 (~r(elem!1, z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12566, 12317, 8866, 11269, 1339, 12418, 12429, 11273, 8520, 65])).
% 2.24/2.48 tff(12568,plain,
% 2.24/2.48 (b(elem!1, z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1759, 12567, 3768])).
% 2.24/2.48 tff(12569,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1908, 12568, 12433, 12431])).
% 2.24/2.48 tff(12570,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[857, 12569, 12429])).
% 2.24/2.48 tff(12571,plain,
% 2.24/2.48 (~r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8151, 12570, 1339])).
% 2.24/2.48 tff(12572,plain,
% 2.24/2.48 (s(s(s(z))) = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2463, 12571, 12425])).
% 2.24/2.48 tff(12573,plain,
% 2.24/2.48 (s(s(s(s(z)))) = s(elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12572])).
% 2.24/2.48 tff(12574,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12573])).
% 2.24/2.48 tff(12575,plain,
% 2.24/2.48 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12572])).
% 2.24/2.48 tff(12576,plain,
% 2.24/2.48 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.24/2.48 inference(transitivity,[status(thm)],[12575, 2115])).
% 2.24/2.48 tff(12577,plain,
% 2.24/2.48 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12576])).
% 2.24/2.48 tff(12578,plain,
% 2.24/2.48 (~(s(s(z)) = elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[2009, 12577])).
% 2.24/2.48 tff(12579,plain,
% 2.24/2.48 (~r(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12443, 12429, 12431, 65, 11269, 8866])).
% 2.24/2.48 tff(12580,plain,
% 2.24/2.48 (b(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12313, 12579, 11273])).
% 2.24/2.48 tff(12581,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12572])).
% 2.24/2.48 tff(12582,plain,
% 2.24/2.48 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[1339, 12581])).
% 2.24/2.48 tff(12583,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4236, 12582, 12580, 12578, 12418, 11269])).
% 2.24/2.48 tff(12584,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2268, 12583])).
% 2.24/2.48 tff(12585,plain,
% 2.24/2.48 (b(s(s(z)), s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12584, 12574])).
% 2.24/2.48 tff(12586,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12573])).
% 2.24/2.48 tff(12587,plain,
% 2.24/2.48 (b(s(elem!1), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12433, 12586])).
% 2.24/2.48 tff(12588,plain,
% 2.24/2.48 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12573])).
% 2.24/2.48 tff(12589,plain,
% 2.24/2.48 (b(z, s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12431, 12588])).
% 2.24/2.48 tff(12590,plain,
% 2.24/2.48 (~r(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12449, 8520, 12369])).
% 2.24/2.48 tff(12591,plain,
% 2.24/2.48 (b(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2229, 12590])).
% 2.24/2.48 tff(12592,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12471, 12425, 12591, 12418, 12580, 11273, 12317, 5308])).
% 2.24/2.48 tff(12593,plain,
% 2.24/2.48 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12573])).
% 2.24/2.48 tff(12594,plain,
% 2.24/2.48 (r(elem!1, s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12582, 12593])).
% 2.24/2.48 tff(12595,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7671, 12572, 5725])).
% 2.24/2.48 tff(12596,plain,
% 2.24/2.48 (~(s(elem!1) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[264, 12592])).
% 2.24/2.48 tff(12597,plain,
% 2.24/2.48 (s(s(s(s(z)))) = s(elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1472, 12572])).
% 2.24/2.48 tff(12598,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[804])).
% 2.24/2.48 tff(12599,plain,
% 2.24/2.48 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[12598])).
% 2.24/2.48 tff(12600,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[2520, 12599])).
% 2.24/2.48 tff(12601,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[229, 12600])).
% 2.24/2.48 tff(12602,plain,((~b(s(elem!1), elem!1)) | b(s(s(s(s(z)))), elem!1) | (~(s(s(s(s(z)))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(12603,plain,
% 2.24/2.48 (~b(s(elem!1), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12602, 12597, 12569])).
% 2.24/2.48 tff(12604,plain,
% 2.24/2.48 (r(s(elem!1), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[270, 12603, 12596])).
% 2.24/2.48 tff(12605,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12573])).
% 2.24/2.48 tff(12606,plain,
% 2.24/2.48 (r(s(elem!1), s(z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8520, 12605])).
% 2.24/2.48 tff(12607,plain,
% 2.24/2.48 (~b(z, s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8043, 12606, 12369, 12418, 12604, 12592, 12595, 12580, 12589])).
% 2.24/2.48 tff(12608,plain,
% 2.24/2.48 (r(z, s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[146, 12607])).
% 2.24/2.48 tff(12609,plain,
% 2.24/2.48 (~r(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[306, 12608, 8866])).
% 2.24/2.48 tff(12610,plain,
% 2.24/2.48 (b(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1970, 12609])).
% 2.24/2.48 tff(12611,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8492, 12610, 12604, 12595, 12418, 12594])).
% 2.24/2.48 tff(12612,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[363, 12611, 12592])).
% 2.24/2.48 tff(12613,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12614,plain,
% 2.24/2.48 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(12615,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12614])).
% 2.24/2.48 tff(12616,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[12615, 12613])).
% 2.24/2.48 tff(12617,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(12618,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[12617, 12616])).
% 2.24/2.48 tff(12619,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[12618, 337, 12612, 12589, 12587, 12585])).
% 2.24/2.48 tff(12620,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[12572])).
% 2.24/2.48 tff(12621,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10705, 337, 11273, 12591, 11272])).
% 2.24/2.48 tff(12622,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4268, 12621])).
% 2.24/2.49 tff(12623,plain,
% 2.24/2.49 (r(s(s(z)), elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12622, 12620])).
% 2.24/2.49 tff(12624,plain,
% 2.24/2.49 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1979, 12610, 12580, 12418])).
% 2.24/2.49 tff(12625,plain,
% 2.24/2.49 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[350, 12624, 12595])).
% 2.24/2.49 tff(12626,plain,
% 2.24/2.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12627,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12628,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12627, 12626])).
% 2.24/2.49 tff(12629,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12628, 189, 12625, 12623])).
% 2.24/2.49 tff(12630,plain,
% 2.24/2.49 (elem!1 = s(s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12572, 5931])).
% 2.24/2.49 tff(12631,plain,
% 2.24/2.49 (~(s(s(z)) = s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8616, 12630])).
% 2.24/2.49 tff(12632,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2317, 43, 12631, 12629, 12619])).
% 2.24/2.49 tff(12633,plain,((z = elem!1) | (~r(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(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(12634,plain,
% 2.24/2.49 (z = elem!1),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12633, 8519, 1339, 5641, 6683])).
% 2.24/2.49 tff(12635,plain,
% 2.24/2.49 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12634])).
% 2.24/2.49 tff(12636,plain,
% 2.24/2.49 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.24/2.49 inference(symmetry,[status(thm)],[12635])).
% 2.24/2.49 tff(12637,plain,
% 2.24/2.49 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12634])).
% 2.24/2.49 tff(12638,plain,
% 2.24/2.49 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12637, 2114])).
% 2.24/2.49 tff(12639,plain,
% 2.24/2.49 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12638])).
% 2.24/2.49 tff(12640,plain,
% 2.24/2.49 (~(elem!1 = s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[31, 12639])).
% 2.24/2.49 tff(12641,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10709, 12622, 1339])).
% 2.24/2.49 tff(12642,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2268, 12641])).
% 2.24/2.49 tff(12643,plain,
% 2.24/2.49 (b(elem!1, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10167, 12634, 12431])).
% 2.24/2.49 tff(12644,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3698, 337, 11273, 12591, 11272])).
% 2.24/2.49 tff(12645,plain,
% 2.24/2.49 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2854, 12644])).
% 2.24/2.49 tff(12646,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10873, 12645, 1339])).
% 2.24/2.49 tff(12647,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9040, 12646])).
% 2.24/2.49 tff(12648,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12649,plain,
% 2.24/2.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12650,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12649])).
% 2.24/2.49 tff(12651,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12650, 12648])).
% 2.24/2.49 tff(12652,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12653,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12652, 12651])).
% 2.24/2.49 tff(12654,plain,
% 2.24/2.49 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12653, 337, 12647, 12643, 12591])).
% 2.24/2.49 tff(12655,plain,
% 2.24/2.49 (~b(elem!1, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12654, 12642])).
% 2.24/2.49 tff(12656,plain,
% 2.24/2.49 (r(elem!1, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9064, 12655, 12640])).
% 2.24/2.49 tff(12657,plain,
% 2.24/2.49 (r(z, s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12656, 12636])).
% 2.24/2.49 tff(12658,plain,
% 2.24/2.49 (~r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3378, 12657, 12369])).
% 2.24/2.49 tff(12659,plain,
% 2.24/2.49 (b(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8207, 12658])).
% 2.24/2.49 tff(12660,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10893, 12659, 11273, 1339, 11269])).
% 2.24/2.49 tff(12661,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6726, 12660, 10026])).
% 2.24/2.49 tff(12662,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12634])).
% 2.24/2.49 tff(12663,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12433, 12662])).
% 2.24/2.49 tff(12664,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, 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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, 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(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12665,plain,
% 2.24/2.49 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, 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(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12666,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, 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(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12665])).
% 2.24/2.49 tff(12667,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, 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(s(z)))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12666, 12664])).
% 2.24/2.49 tff(12668,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12669,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, 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(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12668, 12667])).
% 2.24/2.49 tff(12670,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12669, 337, 12663, 12642, 12643, 12661])).
% 2.24/2.49 tff(12671,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10038, 43, 10035, 12670])).
% 2.24/2.49 tff(12672,plain,
% 2.24/2.49 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12634])).
% 2.24/2.49 tff(12673,plain,
% 2.24/2.49 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12672, 10040])).
% 2.24/2.49 tff(12674,plain,
% 2.24/2.49 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.49 inference(transitivity,[status(thm)],[12673, 10041])).
% 2.24/2.49 tff(12675,plain,
% 2.24/2.49 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12674])).
% 2.24/2.49 tff(12676,plain,
% 2.24/2.49 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10047, 12675])).
% 2.24/2.49 tff(12677,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11168, 337, 12663, 12643, 12661])).
% 2.24/2.49 tff(12678,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10056, 12677, 12676])).
% 2.24/2.49 tff(12679,plain,
% 2.24/2.49 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.24/2.49 inference(transitivity,[status(thm)],[12638, 2115])).
% 2.24/2.49 tff(12680,plain,
% 2.24/2.49 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12679])).
% 2.24/2.49 tff(12681,plain,
% 2.24/2.49 (~(s(s(z)) = elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[31, 12680])).
% 2.24/2.49 tff(12682,plain,
% 2.24/2.49 (~b(s(s(z)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5151, 337, 12663, 12642, 12643])).
% 2.24/2.49 tff(12683,plain,
% 2.24/2.49 (r(s(s(z)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2301, 12682, 12681])).
% 2.24/2.49 tff(12684,plain,
% 2.24/2.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12685,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12686,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12685, 12684])).
% 2.24/2.49 tff(12687,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12686, 189, 12683, 12678, 12671])).
% 2.24/2.49 tff(12688,plain,(b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(z))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(12689,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12688, 1339, 5641, 6683])).
% 2.24/2.49 tff(12690,plain,
% 2.24/2.49 (~r(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1580, 1115, 1141])).
% 2.24/2.49 tff(12691,plain,
% 2.24/2.49 (b(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[80, 12690])).
% 2.24/2.49 tff(12692,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12353, 337, 12691, 5125, 1658, 3690])).
% 2.24/2.49 tff(12693,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(12694,plain,
% 2.24/2.49 (~r(z, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12693, 1339, 1658, 1141])).
% 2.24/2.49 tff(12695,plain,
% 2.24/2.49 (b(z, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1786, 12694])).
% 2.24/2.49 tff(12696,plain,
% 2.24/2.49 (~(s(s(s(s(z)))) = elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8641, 4370, 1231])).
% 2.24/2.49 tff(12697,plain,
% 2.24/2.49 (~r(s(z), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12443, 12696, 12695, 65, 1141, 275])).
% 2.24/2.49 tff(12698,plain,
% 2.24/2.49 (b(s(z), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12313, 12697, 1658])).
% 2.24/2.49 tff(12699,plain,
% 2.24/2.49 (~r(elem!1, z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3859, 5940, 275])).
% 2.24/2.49 tff(12700,plain,
% 2.24/2.49 (b(elem!1, z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1759, 12699, 3768])).
% 2.24/2.49 tff(12701,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12702,plain,
% 2.24/2.49 (((~b(s(s(s(z))), s(z))) | (~b(s(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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12703,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12702])).
% 2.24/2.49 tff(12704,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12703, 12701])).
% 2.24/2.49 tff(12705,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12706,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12705, 12704])).
% 2.24/2.49 tff(12707,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12706, 337, 1301, 1231, 1592, 1658, 10691])).
% 2.24/2.49 tff(12708,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(12709,plain,
% 2.24/2.49 (~b(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12708, 1231, 12695, 1658, 3690])).
% 2.24/2.49 tff(12710,plain,
% 2.24/2.49 (r(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[80, 12709])).
% 2.24/2.49 tff(12711,plain,
% 2.24/2.49 (~r(z, elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[785, 5940, 12710])).
% 2.24/2.49 tff(12712,plain,
% 2.24/2.49 (b(z, elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[921, 12711, 65])).
% 2.24/2.49 tff(12713,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12714,plain,
% 2.24/2.49 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(12715,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12714])).
% 2.24/2.49 tff(12716,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[12715, 12713])).
% 2.24/2.49 tff(12717,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(12718,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[12717, 12716])).
% 2.24/2.49 tff(12719,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12718, 337, 925, 1763, 791, 2454])).
% 2.24/2.49 tff(12720,plain,
% 2.24/2.49 (r(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[48, 12719])).
% 2.24/2.49 tff(12721,plain,
% 2.24/2.49 (~b(s(s(s(z))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2069, 337, 925, 1763, 2454])).
% 2.24/2.49 tff(12722,plain,
% 2.24/2.49 (r(s(s(s(z))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1498, 12721])).
% 2.24/2.49 tff(12723,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1316, 189, 275, 12722, 12720])).
% 2.24/2.49 tff(12724,plain,((~b(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,[]))).
% 2.24/2.49 tff(12725,plain,
% 2.24/2.49 (~b(s(s(s(z))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12724, 12712, 12700, 12698, 275])).
% 2.24/2.49 tff(12726,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2992, 12712, 12695, 12700])).
% 2.24/2.49 tff(12727,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[857, 12726, 12696])).
% 2.24/2.49 tff(12728,plain,
% 2.24/2.49 (~r(s(s(s(z))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8151, 12727, 1339])).
% 2.24/2.49 tff(12729,plain,
% 2.24/2.49 (s(s(s(z))) = elem!1),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2463, 12728, 12725])).
% 2.24/2.49 tff(12730,plain,
% 2.24/2.49 (s(s(s(s(z)))) = s(elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1472, 12729])).
% 2.24/2.49 tff(12731,plain,
% 2.24/2.49 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12730])).
% 2.24/2.49 tff(12732,plain,
% 2.24/2.49 (s(s(s(z))) = elem!1),
% 2.24/2.49 inference(transitivity,[status(thm)],[162, 12731, 91])).
% 2.24/2.49 tff(12733,plain,
% 2.24/2.49 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12732])).
% 2.24/2.49 tff(12734,plain,
% 2.24/2.49 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.24/2.49 inference(symmetry,[status(thm)],[12733])).
% 2.24/2.49 tff(12735,plain,
% 2.24/2.49 ((~b(elem!1, s(z))) <=> (~b(s(s(s(z))), s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[12734])).
% 2.24/2.49 tff(12736,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(z))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[4370, 12735])).
% 2.24/2.49 tff(12737,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1658, 12736])).
% 2.24/2.49 tff(12738,plain,(b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (z = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(12739,plain,
% 2.24/2.49 (b(elem!1, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12738, 65, 1339, 8866, 11273, 11269, 12689, 12317])).
% 2.24/2.49 tff(12740,plain,
% 2.24/2.49 (~b(s(s(s(z))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[12424, 337, 12739, 11273, 11272])).
% 2.24/2.49 tff(12741,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12742,plain,
% 2.34/2.50 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12743,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12742])).
% 2.34/2.50 tff(12744,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12743, 12741])).
% 2.34/2.50 tff(12745,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12746,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12745, 12744])).
% 2.34/2.50 tff(12747,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12746, 337, 12739, 12689, 11273, 11272])).
% 2.34/2.50 tff(12748,plain,
% 2.34/2.50 (s(s(s(s(z)))) = elem!1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12443, 1735, 12695, 65, 1141, 275])).
% 2.34/2.50 tff(12749,plain,
% 2.34/2.50 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12748])).
% 2.34/2.50 tff(12750,plain,
% 2.34/2.50 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(symmetry,[status(thm)],[12749])).
% 2.34/2.50 tff(12751,plain,
% 2.34/2.50 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12750])).
% 2.34/2.50 tff(12752,plain,
% 2.34/2.50 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12748])).
% 2.34/2.50 tff(12753,plain,
% 2.34/2.50 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12752, 2114])).
% 2.34/2.50 tff(12754,plain,
% 2.34/2.50 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[12753, 2115])).
% 2.34/2.50 tff(12755,plain,
% 2.34/2.50 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12754])).
% 2.34/2.50 tff(12756,plain,
% 2.34/2.50 (~(s(s(z)) = elem!1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[2263, 12755])).
% 2.34/2.50 tff(12757,plain,
% 2.34/2.50 (~r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12343, 2245, 275])).
% 2.34/2.50 tff(12758,plain,
% 2.34/2.50 (b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2242, 12757])).
% 2.34/2.50 tff(12759,plain,
% 2.34/2.50 (((~b(elem!1, z)) | (~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)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12760,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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(X1, 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))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12759])).
% 2.34/2.50 tff(12761,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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(X1, 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)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12760, 8237])).
% 2.34/2.50 tff(12762,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12763,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12762, 12761])).
% 2.34/2.50 tff(12764,plain,
% 2.34/2.50 (~b(s(s(z)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12763, 337, 925, 1763, 12758])).
% 2.34/2.50 tff(12765,plain,
% 2.34/2.50 (r(s(s(z)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2301, 12764, 4103])).
% 2.34/2.50 tff(12766,plain,
% 2.34/2.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12767,plain,
% 2.34/2.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12768,plain,
% 2.34/2.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12767, 12766])).
% 2.34/2.50 tff(12769,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12768, 189, 1735, 12765, 2245])).
% 2.34/2.50 tff(12770,plain,((~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(12771,plain,
% 2.34/2.50 (~r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12770, 1735, 12756, 9182, 12441, 275])).
% 2.34/2.50 tff(12772,plain,
% 2.34/2.50 (b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2229, 12771])).
% 2.34/2.50 tff(12773,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12774,plain,
% 2.34/2.50 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12775,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12774])).
% 2.34/2.50 tff(12776,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12775, 12773])).
% 2.34/2.50 tff(12777,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12778,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12777, 12776])).
% 2.34/2.50 tff(12779,plain,
% 2.34/2.50 (~b(s(s(z)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12778, 337, 327, 1658, 12772, 3690])).
% 2.34/2.50 tff(12780,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12779, 12751])).
% 2.34/2.50 tff(12781,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10705, 337, 1658, 12772, 3690])).
% 2.34/2.50 tff(12782,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4268, 12781])).
% 2.34/2.50 tff(12783,plain,
% 2.34/2.50 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10709, 12782, 1339])).
% 2.34/2.50 tff(12784,plain,
% 2.34/2.50 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2268, 12783])).
% 2.34/2.50 tff(12785,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12784, 12780])).
% 2.34/2.50 tff(12786,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (z = elem!1) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(12787,plain,
% 2.34/2.50 (~r(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12786, 12739, 11273, 1339, 8866, 65, 11269])).
% 2.34/2.50 tff(12788,plain,
% 2.34/2.50 (b(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12313, 12787, 11273])).
% 2.34/2.50 tff(12789,plain,
% 2.34/2.50 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5643, 12788, 5641])).
% 2.34/2.50 tff(12790,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[857, 12789, 12747])).
% 2.34/2.50 tff(12791,plain,
% 2.34/2.50 (~r(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8151, 12790, 1339])).
% 2.34/2.50 tff(12792,plain,
% 2.34/2.50 (s(s(s(z))) = elem!1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2463, 12791, 12740])).
% 2.34/2.50 tff(12793,plain,
% 2.34/2.50 (s(s(s(s(z)))) = s(elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1472, 12792])).
% 2.34/2.50 tff(12794,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2743, 12793, 12317])).
% 2.34/2.50 tff(12795,plain,
% 2.34/2.50 (~(s(elem!1) = elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7666, 12792, 12789])).
% 2.34/2.50 tff(12796,plain,
% 2.34/2.50 (~b(s(elem!1), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12602, 12793, 12747])).
% 2.34/2.50 tff(12797,plain,
% 2.34/2.50 (r(s(elem!1), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[270, 12796, 12795])).
% 2.34/2.50 tff(12798,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7671, 12792, 5725])).
% 2.34/2.50 tff(12799,plain,
% 2.34/2.50 (s(s(s(s(z)))) = s(elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12792])).
% 2.34/2.50 tff(12800,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12799])).
% 2.34/2.50 tff(12801,plain,
% 2.34/2.50 (b(s(elem!1), s(z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12689, 12800])).
% 2.34/2.50 tff(12802,plain,
% 2.34/2.50 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12799])).
% 2.34/2.50 tff(12803,plain,
% 2.34/2.50 (~r(z, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12693, 1339, 11273, 11269])).
% 2.34/2.50 tff(12804,plain,
% 2.34/2.50 (b(z, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1786, 12803])).
% 2.34/2.50 tff(12805,plain,
% 2.34/2.50 (b(z, s(elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12804, 12802])).
% 2.34/2.50 tff(12806,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[1470])).
% 2.34/2.50 tff(12807,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.50 inference(symmetry,[status(thm)],[12806])).
% 2.34/2.50 tff(12808,plain,
% 2.34/2.50 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1979, 326, 791, 327])).
% 2.34/2.50 tff(12809,plain,
% 2.34/2.50 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1970, 12808])).
% 2.34/2.50 tff(12810,plain,
% 2.34/2.50 (~r(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[306, 12809, 275])).
% 2.34/2.50 tff(12811,plain,
% 2.34/2.50 (b(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[146, 12810])).
% 2.34/2.50 tff(12812,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8390, 337, 326, 600, 1544, 791, 12811])).
% 2.34/2.50 tff(12813,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[363, 12812, 172])).
% 2.34/2.50 tff(12814,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12813, 12807])).
% 2.34/2.50 tff(12815,plain,
% 2.34/2.50 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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(z))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12816,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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(X1, 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(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12815])).
% 2.34/2.50 tff(12817,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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(X1, 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(z))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12816, 767])).
% 2.34/2.50 tff(12818,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12819,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12818, 12817])).
% 2.34/2.50 tff(12820,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12819, 337, 327, 326, 791])).
% 2.34/2.50 tff(12821,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8966, 12820])).
% 2.34/2.50 tff(12822,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 2.34/2.50 tff(12823,plain,
% 2.34/2.50 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12824,plain,
% 2.34/2.50 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12825,plain,
% 2.34/2.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12824])).
% 2.34/2.50 tff(12826,plain,
% 2.34/2.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12825, 12823])).
% 2.34/2.50 tff(12827,plain,
% 2.34/2.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12828,plain,
% 2.34/2.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12827, 12826])).
% 2.34/2.50 tff(12829,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12828, 189, 1141, 214, 12822])).
% 2.34/2.50 tff(12830,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(12831,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12830, 12821, 1141])).
% 2.34/2.50 tff(12832,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12831, 12814])).
% 2.34/2.50 tff(12833,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(12834,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12833, 12792, 11269, 12794, 12805, 12801, 12788, 12739, 8866])).
% 2.34/2.50 tff(12835,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[350, 12834, 12798])).
% 2.34/2.50 tff(12836,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[358, 12835, 12797])).
% 2.34/2.50 tff(12837,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[363, 12836, 12794])).
% 2.34/2.50 tff(12838,plain,
% 2.34/2.50 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12799])).
% 2.34/2.50 tff(12839,plain,
% 2.34/2.50 (~(elem!1 = s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2760, 12789])).
% 2.34/2.50 tff(12840,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12841,plain,
% 2.34/2.50 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(12842,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[12841])).
% 2.34/2.50 tff(12843,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[12842, 12840])).
% 2.34/2.50 tff(12844,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), 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)))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(12845,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12844, 12843])).
% 2.34/2.50 tff(12846,plain,
% 2.34/2.50 (~b(elem!1, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12845, 337, 12739, 12689, 11273, 11272])).
% 2.34/2.50 tff(12847,plain,
% 2.34/2.50 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2845, 43, 12846])).
% 2.34/2.50 tff(12848,plain,
% 2.34/2.50 (r(elem!1, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[12847, 12839])).
% 2.34/2.50 tff(12849,plain,
% 2.34/2.50 (r(elem!1, s(elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[12848, 12838])).
% 2.34/2.50 tff(12850,plain,
% 2.34/2.50 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[427, 12794])).
% 2.34/2.51 tff(12851,plain,
% 2.34/2.51 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[991, 189, 12797, 12835])).
% 2.34/2.51 tff(12852,plain,
% 2.34/2.51 (b(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[579, 12851, 12850])).
% 2.34/2.51 tff(12853,plain,
% 2.34/2.51 (~b(z, s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8033, 12852, 12797, 12798, 12805, 12849, 12794])).
% 2.34/2.51 tff(12854,plain,
% 2.34/2.51 (r(z, s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[146, 12853])).
% 2.34/2.51 tff(12855,plain,
% 2.34/2.51 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[306, 12854, 8866])).
% 2.34/2.51 tff(12856,plain,
% 2.34/2.51 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1970, 12855])).
% 2.34/2.51 tff(12857,plain,
% 2.34/2.51 (~b(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12708, 12689, 12804, 11273, 11272])).
% 2.34/2.51 tff(12858,plain,
% 2.34/2.51 (r(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[80, 12857])).
% 2.34/2.51 tff(12859,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[223, 12854, 12858])).
% 2.34/2.51 tff(12860,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8966, 12859])).
% 2.34/2.51 tff(12861,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2144, 12860, 12856, 12801, 12837])).
% 2.34/2.51 tff(12862,plain,((z = elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(z))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12863,plain,
% 2.34/2.51 (z = elem!1),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12862, 1339, 5641, 6683])).
% 2.34/2.51 tff(12864,plain,
% 2.34/2.51 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12863])).
% 2.34/2.51 tff(12865,plain,
% 2.34/2.51 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12864, 2114])).
% 2.34/2.51 tff(12866,plain,
% 2.34/2.51 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[12865, 2115])).
% 2.34/2.51 tff(12867,plain,
% 2.34/2.51 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12866])).
% 2.34/2.51 tff(12868,plain,
% 2.34/2.51 (~(s(s(z)) = elem!1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[31, 12867])).
% 2.34/2.51 tff(12869,plain,
% 2.34/2.51 (~b(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10711, 1339, 11273, 11272, 12689])).
% 2.34/2.51 tff(12870,plain,
% 2.34/2.51 (r(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2229, 12869])).
% 2.34/2.51 tff(12871,plain,
% 2.34/2.51 (r(elem!1, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3068, 12863, 12858])).
% 2.34/2.51 tff(12872,plain,
% 2.34/2.51 (~r(s(s(z)), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5156, 189, 12871, 12870])).
% 2.34/2.51 tff(12873,plain,
% 2.34/2.51 (b(s(s(z)), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2301, 12872, 12868])).
% 2.34/2.51 tff(12874,plain,
% 2.34/2.51 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10167, 12863, 12804])).
% 2.34/2.51 tff(12875,plain,
% 2.34/2.51 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12863])).
% 2.34/2.51 tff(12876,plain,
% 2.34/2.51 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12875])).
% 2.34/2.51 tff(12877,plain,
% 2.34/2.51 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[817, 12876])).
% 2.34/2.51 tff(12878,plain,
% 2.34/2.51 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12863])).
% 2.34/2.51 tff(12879,plain,
% 2.34/2.51 (r(s(z), elem!1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8866, 12878])).
% 2.34/2.51 tff(12880,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2089, 12879, 11269])).
% 2.34/2.51 tff(12881,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[857, 12880, 12877])).
% 2.34/2.51 tff(12882,plain,
% 2.34/2.51 (((~b(s(s(s(s(z)))), elem!1)) | (~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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), 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)), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12883,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12882])).
% 2.34/2.51 tff(12884,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12883, 5146])).
% 2.34/2.51 tff(12885,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(12886,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[12885, 12884])).
% 2.34/2.51 tff(12887,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12886, 337, 12881, 12874, 12873])).
% 2.34/2.51 tff(12888,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2268, 12887])).
% 2.34/2.51 tff(12889,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10709, 12888, 1339])).
% 2.34/2.51 tff(12890,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4268, 12889])).
% 2.34/2.51 tff(12891,plain,
% 2.34/2.51 (~r(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10137, 12888, 11269])).
% 2.34/2.51 tff(12892,plain,
% 2.34/2.51 (b(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8207, 12891])).
% 2.34/2.51 tff(12893,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12894,plain,
% 2.34/2.51 (((~b(s(z), s(s(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(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12895,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12894])).
% 2.34/2.51 tff(12896,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12895, 12893])).
% 2.34/2.51 tff(12897,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(z)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(12898,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[12897, 12896])).
% 2.34/2.51 tff(12899,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12898, 337, 12892, 11273, 12890, 11272])).
% 2.34/2.51 tff(12900,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(z))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12901,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12900, 5641, 10896])).
% 2.34/2.51 tff(12902,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[548, 12901])).
% 2.34/2.51 tff(12903,plain,
% 2.34/2.51 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10151, 4332, 1141, 4222])).
% 2.34/2.51 tff(12904,plain,
% 2.34/2.51 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10027, 12903])).
% 2.34/2.51 tff(12905,plain,
% 2.34/2.51 (~r(s(s(s(s(s(z))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3330, 189, 1115, 7908])).
% 2.34/2.51 tff(12906,plain,
% 2.34/2.51 (b(s(s(s(s(s(z))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 12905])).
% 2.34/2.51 tff(12907,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3896, 189, 10897, 1141, 1115])).
% 2.34/2.51 tff(12908,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12909,plain,
% 2.34/2.51 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12908, 1115])).
% 2.34/2.51 tff(12910,plain,
% 2.34/2.51 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1150, 12909])).
% 2.34/2.51 tff(12911,plain,
% 2.34/2.51 (~r(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8078, 811, 1115])).
% 2.34/2.51 tff(12912,plain,
% 2.34/2.51 (b(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[80, 12911])).
% 2.34/2.51 tff(12913,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12914,plain,
% 2.34/2.51 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12915,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12914])).
% 2.34/2.51 tff(12916,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12915, 12913])).
% 2.34/2.51 tff(12917,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(12918,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[12917, 12916])).
% 2.34/2.51 tff(12919,plain,
% 2.34/2.51 (~b(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12918, 337, 12912, 12910, 1342, 10299])).
% 2.34/2.51 tff(12920,plain,
% 2.34/2.51 (r(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8207, 12919])).
% 2.34/2.51 tff(12921,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12922,plain,
% 2.34/2.51 (((~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)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12923,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12922])).
% 2.34/2.51 tff(12924,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12923, 12921])).
% 2.34/2.51 tff(12925,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(12926,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[12925, 12924])).
% 2.34/2.51 tff(12927,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12926, 189, 811, 1397, 3370])).
% 2.34/2.51 tff(12928,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12929,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12928, 811, 12920])).
% 2.34/2.51 tff(12930,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9040, 12929])).
% 2.34/2.51 tff(12931,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12932,plain,
% 2.34/2.51 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(12933,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[12932])).
% 2.34/2.51 tff(12934,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~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(X1, 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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[12933, 12931])).
% 2.34/2.51 tff(12935,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(12936,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[12935, 12934])).
% 2.34/2.51 tff(12937,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12936, 337, 12912, 12910, 12930, 4340, 1342, 10299])).
% 2.34/2.51 tff(12938,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12939,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12938, 4222, 1342, 1115])).
% 2.34/2.51 tff(12940,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[851, 12939])).
% 2.34/2.51 tff(12941,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1281, 337, 1275, 2, 1231, 11268])).
% 2.34/2.51 tff(12942,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12943,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12942, 12940, 12910])).
% 2.34/2.51 tff(12944,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[548, 12943])).
% 2.34/2.51 tff(12945,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10709, 12944, 4222])).
% 2.34/2.51 tff(12946,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4268, 12945])).
% 2.34/2.51 tff(12947,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7507, 12946, 1115, 12944, 1342])).
% 2.34/2.51 tff(12948,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2854, 12947])).
% 2.34/2.51 tff(12949,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1355, 189, 12944, 4222, 12948])).
% 2.34/2.51 tff(12950,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(12951,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12950, 1342, 1115])).
% 2.34/2.51 tff(12952,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2268, 12951])).
% 2.34/2.51 tff(12953,plain,
% 2.34/2.51 (~b(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[12918, 337, 1301, 1275, 1342, 3357])).
% 2.34/2.51 tff(12954,plain,
% 2.34/2.51 (r(s(z), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8207, 12953])).
% 2.34/2.52 tff(12955,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12928, 12954, 811])).
% 2.34/2.52 tff(12956,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9040, 12955])).
% 2.34/2.52 tff(12957,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(12958,plain,
% 2.34/2.52 (((~b(s(s(z)), s(s(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(s(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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(12959,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[12958])).
% 2.34/2.52 tff(12960,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[12959, 12957])).
% 2.34/2.52 tff(12961,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(12962,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[12961, 12960])).
% 2.34/2.52 tff(12963,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12962, 337, 1275, 1396, 12956, 3357])).
% 2.34/2.52 tff(12964,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(12965,plain,
% 2.34/2.52 (~b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12964, 811, 12952, 12910, 12912, 1342])).
% 2.34/2.52 tff(12966,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2229, 12965])).
% 2.34/2.52 tff(12967,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10440, 189, 811, 12966])).
% 2.34/2.52 tff(12968,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9040, 12967])).
% 2.34/2.52 tff(12969,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1209, 337, 12952, 12968, 1342])).
% 2.34/2.52 tff(12970,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1792, 12969])).
% 2.34/2.52 tff(12971,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(12972,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(12973,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[12972, 12971])).
% 2.34/2.52 tff(12974,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12973, 189, 10897, 811, 12970])).
% 2.34/2.52 tff(12975,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(12976,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12975, 1342, 1115])).
% 2.34/2.52 tff(12977,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[851, 12976])).
% 2.34/2.52 tff(12978,plain,
% 2.34/2.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12942, 12977, 12910])).
% 2.34/2.52 tff(12979,plain,
% 2.34/2.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[548, 12978])).
% 2.34/2.52 tff(12980,plain,
% 2.34/2.52 (~r(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5118, 189, 12979, 1115])).
% 2.34/2.52 tff(12981,plain,
% 2.34/2.52 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[199, 43, 12980])).
% 2.34/2.52 tff(12982,plain,
% 2.34/2.52 (b(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12981, 179])).
% 2.34/2.52 tff(12983,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7911, 189, 12979, 7908])).
% 2.34/2.52 tff(12984,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10155, 12983])).
% 2.34/2.52 tff(12985,plain,
% 2.34/2.52 (~r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5075, 12979, 1115])).
% 2.34/2.52 tff(12986,plain,
% 2.34/2.52 (b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1498, 12985])).
% 2.34/2.52 tff(12987,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(12988,plain,
% 2.34/2.52 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(12989,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[12988])).
% 2.34/2.52 tff(12990,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(transitivity,[status(thm)],[12989, 12987])).
% 2.34/2.52 tff(12991,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(12992,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[12991, 12990])).
% 2.34/2.52 tff(12993,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12992, 337, 1342, 12986, 12984, 12982, 12906])).
% 2.34/2.52 tff(12994,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(12995,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12994, 1342, 1115])).
% 2.34/2.52 tff(12996,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10027, 12995])).
% 2.34/2.52 tff(12997,plain,
% 2.34/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3268, 337, 12910, 12977, 12996])).
% 2.34/2.52 tff(12998,plain,
% 2.34/2.52 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7948, 12997])).
% 2.34/2.52 tff(12999,plain,
% 2.34/2.52 (~b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10521, 12977, 12910, 11268])).
% 2.34/2.52 tff(13000,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2229, 12999])).
% 2.34/2.52 tff(13001,plain,
% 2.34/2.52 (~r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12343, 13000, 10897])).
% 2.34/2.52 tff(13002,plain,
% 2.34/2.52 (b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2242, 13001])).
% 2.34/2.52 tff(13003,plain,
% 2.34/2.52 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(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(z)))) | (~r(z, s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1407, 2009])).
% 2.34/2.52 tff(13004,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13003, 13002, 1115, 1342, 12952, 12979])).
% 2.34/2.52 tff(13005,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9040, 13004])).
% 2.34/2.52 tff(13006,plain,
% 2.34/2.52 (~b(s(z), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11926, 13005, 12952, 12977])).
% 2.34/2.52 tff(13007,plain,
% 2.34/2.52 (r(s(z), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8207, 13006])).
% 2.34/2.52 tff(13008,plain,
% 2.34/2.52 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10658, 337, 12910, 12977, 12952, 12996])).
% 2.34/2.52 tff(13009,plain,
% 2.34/2.52 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10142, 13008])).
% 2.34/2.52 tff(13010,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10666, 189, 13009, 13007, 12998])).
% 2.34/2.52 tff(13011,plain,((~b(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(13012,plain,
% 2.34/2.52 (~b(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13011, 1115])).
% 2.34/2.52 tff(13013,plain,
% 2.34/2.52 (r(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10825, 13012])).
% 2.34/2.52 tff(13014,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13015,plain,
% 2.34/2.52 (((~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(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13016,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[13015])).
% 2.34/2.52 tff(13017,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[13016, 13014])).
% 2.34/2.52 tff(13018,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(13019,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[13018, 13017])).
% 2.34/2.52 tff(13020,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13019, 189, 1116, 1115, 1397])).
% 2.34/2.52 tff(13021,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(13022,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13021, 13013, 1115])).
% 2.34/2.52 tff(13023,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9040, 13022])).
% 2.34/2.52 tff(13024,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1122, 189, 1116, 1115, 4222])).
% 2.34/2.52 tff(13025,plain,((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(13026,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13025, 13013, 1115])).
% 2.34/2.52 tff(13027,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2268, 13026])).
% 2.34/2.52 tff(13028,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13029,plain,
% 2.34/2.52 (((~b(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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(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)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13030,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[13029])).
% 2.34/2.52 tff(13031,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[13030, 13028])).
% 2.34/2.52 tff(13032,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(13033,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[13032, 13031])).
% 2.34/2.52 tff(13034,plain,
% 2.34/2.52 (~b(s(z), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13033, 337, 12910, 13027, 13023])).
% 2.34/2.52 tff(13035,plain,
% 2.34/2.52 (r(s(z), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8207, 13034])).
% 2.34/2.52 tff(13036,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9013, 189, 10897, 13013, 13035])).
% 2.34/2.52 tff(13037,plain,(~r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(13038,plain,
% 2.34/2.52 (b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1786, 13037])).
% 2.34/2.52 tff(13039,plain,
% 2.34/2.52 (~b(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3510, 337, 3243, 2, 13038, 3242])).
% 2.34/2.52 tff(13040,plain,
% 2.34/2.52 (r(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 13039])).
% 2.34/2.52 tff(13041,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13042,plain,
% 2.34/2.52 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)))))) | (~b(s(s(s(z))), s(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13043,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[13042])).
% 2.34/2.52 tff(13044,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(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(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[13043, 13041])).
% 2.34/2.52 tff(13045,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(13046,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[13045, 13044])).
% 2.34/2.52 tff(13047,plain,
% 2.34/2.52 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13046, 337, 3243, 2, 3242])).
% 2.34/2.52 tff(13048,plain,
% 2.34/2.52 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10352, 13047])).
% 2.34/2.52 tff(13049,plain,
% 2.34/2.52 (~b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4311, 337, 3243, 2, 13038])).
% 2.34/2.52 tff(13050,plain,
% 2.34/2.52 (r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1498, 13049])).
% 2.34/2.52 tff(13051,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10361, 189, 13050, 13048, 13040])).
% 2.34/2.52 tff(13052,plain,((~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(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(13053,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[13052, 12904, 2])).
% 2.34/2.52 tff(13054,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[524, 13053])).
% 2.34/2.52 tff(13055,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13056,plain,
% 2.34/2.52 (((~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(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(13057,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13056])).
% 2.34/2.53 tff(13058,plain,
% 2.34/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13057, 13055])).
% 2.34/2.53 tff(13059,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13060,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13059, 13058])).
% 2.34/2.53 tff(13061,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13060, 189, 6489, 1141, 6479])).
% 2.34/2.53 tff(13062,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)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13063,plain,
% 2.34/2.53 (~r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13062, 13054, 1141])).
% 2.34/2.53 tff(13064,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 2.34/2.53 tff(13065,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2796, 43, 13064, 10072, 10690])).
% 2.34/2.53 tff(13066,plain,(b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13067,plain,
% 2.34/2.53 (b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13066, 13063])).
% 2.34/2.53 tff(13068,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13069,plain,
% 2.34/2.53 (((~b(s(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(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13070,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13069])).
% 2.34/2.53 tff(13071,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13070, 13068])).
% 2.34/2.53 tff(13072,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(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))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13073,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13072, 13071])).
% 2.34/2.53 tff(13074,plain,
% 2.34/2.53 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13073, 337, 2, 11268, 4332, 13067])).
% 2.34/2.53 tff(13075,plain,
% 2.34/2.53 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4268, 13074])).
% 2.34/2.53 tff(13076,plain,
% 2.34/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13077,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13078,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13077, 13076])).
% 2.34/2.53 tff(13079,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13078, 189, 13054, 13075, 4222])).
% 2.34/2.53 tff(13080,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13081,plain,
% 2.34/2.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13080, 2, 1141])).
% 2.34/2.53 tff(13082,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2268, 13081])).
% 2.34/2.53 tff(13083,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10240, 1116, 2, 13082, 13038])).
% 2.34/2.53 tff(13084,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[524, 13083])).
% 2.34/2.53 tff(13085,plain,
% 2.34/2.53 (~r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13062, 13084, 1141])).
% 2.34/2.53 tff(13086,plain,
% 2.34/2.53 (b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13066, 13085])).
% 2.34/2.53 tff(13087,plain,
% 2.34/2.53 (~b(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[12708, 1231, 11268, 13038, 13086])).
% 2.34/2.53 tff(13088,plain,
% 2.34/2.53 (r(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[80, 13087])).
% 2.34/2.53 tff(13089,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10401, 189, 173, 1116, 2245])).
% 2.34/2.53 tff(13090,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13091,plain,
% 2.34/2.53 (~r(s(s(z)), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13090, 13088, 1116])).
% 2.34/2.53 tff(13092,plain,
% 2.34/2.53 (b(s(s(z)), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2229, 13091])).
% 2.34/2.53 tff(13093,plain,
% 2.34/2.53 (~r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3547, 189, 1141, 7908])).
% 2.34/2.53 tff(13094,plain,
% 2.34/2.53 (b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7948, 13093])).
% 2.34/2.53 tff(13095,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13096,plain,
% 2.34/2.53 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(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(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13097,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13096])).
% 2.34/2.53 tff(13098,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13097, 13095])).
% 2.34/2.53 tff(13099,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(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)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13100,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13099, 13098])).
% 2.34/2.53 tff(13101,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13100, 337, 1231, 1396, 3357, 13094, 10129])).
% 2.34/2.53 tff(13102,plain,((~r(s(s(s(s(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(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13103,plain,
% 2.34/2.53 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13102, 13092, 13082, 1231, 1141])).
% 2.34/2.53 tff(13104,plain,
% 2.34/2.53 (~r(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3378, 13088, 1116])).
% 2.34/2.53 tff(13105,plain,
% 2.34/2.53 (b(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[8207, 13104])).
% 2.34/2.53 tff(13106,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11926, 13105, 13082, 1231])).
% 2.34/2.53 tff(13107,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9040, 13106])).
% 2.34/2.53 tff(13108,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10583, 189, 6489, 1397, 3301])).
% 2.34/2.53 tff(13109,plain,((~r(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(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13110,plain,
% 2.34/2.53 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13109, 13107, 13084])).
% 2.34/2.53 tff(13111,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4268, 13110])).
% 2.34/2.53 tff(13112,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.53 tff(13113,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13114,plain,
% 2.34/2.53 (((~b(s(s(s(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(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(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13115,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13114])).
% 2.34/2.53 tff(13116,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13115, 13113])).
% 2.34/2.53 tff(13117,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13118,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13117, 13116])).
% 2.34/2.53 tff(13119,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13118, 337, 2, 1396, 3242, 13112, 7403])).
% 2.34/2.53 tff(13120,plain,((~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13121,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13120, 7403, 13082, 3242, 2])).
% 2.34/2.53 tff(13122,plain,
% 2.34/2.53 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[5507])).
% 2.34/2.53 tff(13123,plain,
% 2.34/2.53 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10026, 13122])).
% 2.34/2.53 tff(13124,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5534, 13123])).
% 2.34/2.53 tff(13125,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13124, 13121])).
% 2.34/2.53 tff(13126,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.53 tff(13127,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.53 tff(13128,plain,
% 2.34/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13129,plain,
% 2.34/2.53 (((~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13130,plain,
% 2.34/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13129])).
% 2.34/2.53 tff(13131,plain,
% 2.34/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13130, 13128])).
% 2.34/2.53 tff(13132,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13133,plain,
% 2.34/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13132, 13131])).
% 2.34/2.53 tff(13134,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13133, 189, 1141, 13127, 13126])).
% 2.34/2.53 tff(13135,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13136,plain,
% 2.34/2.53 (~r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13135, 13125, 1141])).
% 2.34/2.53 tff(13137,plain,
% 2.34/2.53 (b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7948, 13136])).
% 2.34/2.53 tff(13138,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13139,plain,
% 2.34/2.53 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(13140,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[13139])).
% 2.34/2.53 tff(13141,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[13140, 13138])).
% 2.34/2.53 tff(13142,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(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))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(13143,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[13142, 13141])).
% 2.34/2.53 tff(13144,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13143, 337, 2, 11268, 3242, 3357, 7403, 13137])).
% 2.34/2.53 tff(13145,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13146,plain,
% 2.34/2.53 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13145, 13092, 2, 13111, 1141])).
% 2.34/2.53 tff(13147,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10027, 13146, 13103])).
% 2.34/2.53 tff(13148,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(13149,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[13148, 1116, 1141, 2])).
% 2.34/2.53 tff(13150,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[851, 13149])).
% 2.34/2.53 tff(13151,plain,
% 2.34/2.53 (~r(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10559, 13150, 13038, 2, 13082])).
% 2.34/2.53 tff(13152,plain,
% 2.34/2.53 (b(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[80, 13151])).
% 2.34/2.53 tff(13153,plain,
% 2.34/2.53 (~b(s(s(z)), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[12336, 13152, 11268, 13086])).
% 2.34/2.53 tff(13154,plain,
% 2.34/2.53 (r(s(s(z)), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2229, 13153])).
% 2.34/2.53 tff(13155,plain,
% 2.34/2.53 (~r(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12343, 13154, 10897])).
% 2.34/2.54 tff(13156,plain,
% 2.34/2.54 (b(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2242, 13155])).
% 2.34/2.54 tff(13157,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10440, 189, 13150, 13154])).
% 2.34/2.54 tff(13158,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9040, 13157])).
% 2.34/2.54 tff(13159,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12365, 337, 13082, 13038, 13158, 13156])).
% 2.34/2.54 tff(13160,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13161,plain,
% 2.34/2.54 (~r(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13160, 2, 1141])).
% 2.34/2.54 tff(13162,plain,
% 2.34/2.54 (b(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10825, 13161])).
% 2.34/2.54 tff(13163,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13164,plain,
% 2.34/2.54 (((~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)))), 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(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13165,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[13164])).
% 2.34/2.54 tff(13166,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[13165, 13163])).
% 2.34/2.54 tff(13167,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(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)))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(13168,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[13167, 13166])).
% 2.34/2.54 tff(13169,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13168, 337, 3243, 2, 1396, 13038, 1342])).
% 2.34/2.54 tff(13170,plain,((~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(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13171,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13170, 2, 13082, 13162])).
% 2.34/2.54 tff(13172,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[524, 13171])).
% 2.34/2.54 tff(13173,plain,
% 2.34/2.54 (~r(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13062, 13172, 1141])).
% 2.34/2.54 tff(13174,plain,
% 2.34/2.54 (b(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13066, 13173])).
% 2.34/2.54 tff(13175,plain,
% 2.34/2.54 (~b(z, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12336, 3357, 11268, 13174])).
% 2.34/2.54 tff(13176,plain,
% 2.34/2.54 (r(z, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[80, 13175])).
% 2.34/2.54 tff(13177,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10559, 13176, 13038, 2, 13082])).
% 2.34/2.54 tff(13178,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10822, 13162, 13038, 13082])).
% 2.34/2.54 tff(13179,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9040, 13178])).
% 2.34/2.54 tff(13180,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13109, 13172, 13179])).
% 2.34/2.54 tff(13181,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4268, 13180])).
% 2.34/2.54 tff(13182,plain,
% 2.34/2.54 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13145, 3357, 2, 13181, 1141])).
% 2.34/2.54 tff(13183,plain,
% 2.34/2.54 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10027, 13182])).
% 2.34/2.54 tff(13184,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13102, 13183, 13082, 3357, 1141])).
% 2.34/2.54 tff(13185,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[851, 13184, 13177])).
% 2.34/2.54 tff(13186,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13187,plain,
% 2.34/2.54 (~b(s(s(z)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13186, 11269, 12902])).
% 2.34/2.54 tff(13188,plain,
% 2.34/2.54 (r(s(s(z)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2229, 13187])).
% 2.34/2.54 tff(13189,plain,
% 2.34/2.54 (~r(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12343, 13188, 10897])).
% 2.34/2.54 tff(13190,plain,
% 2.34/2.54 (b(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2242, 13189])).
% 2.34/2.54 tff(13191,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13080, 12902, 11269])).
% 2.34/2.54 tff(13192,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2268, 13191])).
% 2.34/2.54 tff(13193,plain,
% 2.34/2.54 (~r(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13160, 12902, 11269])).
% 2.34/2.54 tff(13194,plain,
% 2.34/2.54 (b(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10825, 13193])).
% 2.34/2.54 tff(13195,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10822, 13194, 13038, 13192])).
% 2.34/2.54 tff(13196,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9040, 13195])).
% 2.34/2.54 tff(13197,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10440, 189, 811, 1397, 2245])).
% 2.34/2.54 tff(13198,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13199,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13198, 13188, 13196])).
% 2.34/2.54 tff(13200,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[851, 13199])).
% 2.34/2.54 tff(13201,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3674, 337, 13200, 13192, 13038, 13190])).
% 2.34/2.54 tff(13202,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1792, 13201])).
% 2.34/2.54 tff(13203,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13170, 12902, 13192, 13194])).
% 2.34/2.54 tff(13204,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[524, 13203])).
% 2.34/2.54 tff(13205,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13109, 13204, 13196])).
% 2.34/2.54 tff(13206,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4268, 13205])).
% 2.34/2.54 tff(13207,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13208,plain,
% 2.34/2.54 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(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(z, 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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13209,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[13208])).
% 2.34/2.54 tff(13210,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[13209, 13207])).
% 2.34/2.54 tff(13211,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~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(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(13212,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[13211, 13210])).
% 2.34/2.54 tff(13213,plain,
% 2.34/2.54 (~b(s(s(s(z))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13212, 337, 12902, 13192, 13190, 13194, 13206])).
% 2.34/2.54 tff(13214,plain,
% 2.34/2.54 (r(s(s(s(z))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1498, 13213])).
% 2.34/2.54 tff(13215,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7557, 189, 13204, 13214, 13202])).
% 2.34/2.54 tff(13216,plain,(b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13217,plain,
% 2.34/2.54 (~b(s(s(z)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10521, 1231, 13216, 11268])).
% 2.34/2.54 tff(13218,plain,
% 2.34/2.54 (r(s(s(z)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2229, 13217])).
% 2.34/2.54 tff(13219,plain,
% 2.34/2.54 (~r(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12343, 13218, 10897])).
% 2.34/2.54 tff(13220,plain,
% 2.34/2.54 (b(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2242, 13219])).
% 2.34/2.54 tff(13221,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13222,plain,
% 2.34/2.54 (((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13223,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(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(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[13222])).
% 2.34/2.54 tff(13224,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(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(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[13223, 13221])).
% 2.34/2.54 tff(13225,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(13226,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[13225, 13224])).
% 2.34/2.54 tff(13227,plain,
% 2.34/2.54 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13226, 337, 13216, 1231, 3242])).
% 2.34/2.54 tff(13228,plain,
% 2.34/2.54 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 13227])).
% 2.34/2.54 tff(13229,plain,
% 2.34/2.54 (~b(s(s(s(s(s(z))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7939, 337, 13216, 1231, 13038, 3242])).
% 2.34/2.54 tff(13230,plain,
% 2.34/2.54 (r(s(s(s(s(s(z))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 13229])).
% 2.34/2.54 tff(13231,plain,
% 2.34/2.54 (((~b(s(z), s(s(s(s(z)))))) | (~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(s(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))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13232,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[13231])).
% 2.34/2.54 tff(13233,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[13232, 8970])).
% 2.34/2.54 tff(13234,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(13235,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[13234, 13233])).
% 2.34/2.54 tff(13236,plain,
% 2.34/2.54 (~b(z, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13235, 337, 13216, 1231, 13038])).
% 2.34/2.54 tff(13237,plain,
% 2.34/2.54 (r(z, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[80, 13236])).
% 2.34/2.54 tff(13238,plain,
% 2.34/2.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(13239,plain,
% 2.34/2.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(13240,plain,
% 2.34/2.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[13239, 13238])).
% 2.34/2.54 tff(13241,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13240, 189, 13237, 13230, 13228])).
% 2.34/2.54 tff(13242,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13243,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13242, 3242])).
% 2.34/2.54 tff(13244,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[851, 13243])).
% 2.34/2.54 tff(13245,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[12973, 189, 10897, 811, 1168])).
% 2.34/2.54 tff(13246,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(13247,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[13246, 13244])).
% 2.34/2.54 tff(13248,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1792, 13247])).
% 2.34/2.54 tff(13249,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13250,plain,
% 2.34/2.55 (((~b(z, s(s(s(s(z)))))) | (~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13251,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[13250])).
% 2.34/2.55 tff(13252,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[13251, 13249])).
% 2.34/2.55 tff(13253,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(13254,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[13253, 13252])).
% 2.34/2.55 tff(13255,plain,
% 2.34/2.55 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13254, 337, 13216, 13038, 13248, 3242])).
% 2.34/2.55 tff(13256,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10003, 43, 2330, 13255])).
% 2.34/2.55 tff(13257,plain,
% 2.34/2.55 (~b(s(s(s(s(s(z))))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10337, 337, 13038, 13248, 3242])).
% 2.34/2.55 tff(13258,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10341, 43, 10047, 13257])).
% 2.34/2.55 tff(13259,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3874, 337, 1301, 13216, 13038, 1591])).
% 2.34/2.55 tff(13260,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(13261,plain,
% 2.34/2.55 (~b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13260, 13248])).
% 2.34/2.55 tff(13262,plain,
% 2.34/2.55 (r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[80, 13261])).
% 2.34/2.55 tff(13263,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13240, 189, 13262, 13258, 13256])).
% 2.34/2.55 tff(13264,plain,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(13265,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10027, 13264])).
% 2.34/2.55 tff(13266,plain,
% 2.34/2.55 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12942, 1231, 13216])).
% 2.34/2.55 tff(13267,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[548, 13266])).
% 2.34/2.55 tff(13268,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10709, 1339, 4222])).
% 2.34/2.55 tff(13269,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4268, 13268])).
% 2.34/2.55 tff(13270,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1355, 189, 1339, 4222])).
% 2.34/2.55 tff(13271,plain,
% 2.34/2.55 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2854, 13270])).
% 2.34/2.55 tff(13272,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(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(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13273,plain,
% 2.34/2.55 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13274,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(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(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[13273])).
% 2.34/2.55 tff(13275,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(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(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[13274, 13272])).
% 2.34/2.55 tff(13276,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(13277,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[13276, 13275])).
% 2.34/2.55 tff(13278,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13277, 337, 10143, 13271, 13269, 10630, 10121])).
% 2.34/2.55 tff(13279,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(13280,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13279, 13267, 13265])).
% 2.34/2.55 tff(13281,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2268, 13280])).
% 2.34/2.55 tff(13282,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2827, 337, 13216, 1231, 13281, 13038, 13220])).
% 2.34/2.55 tff(13283,plain,(~b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(13284,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[851, 13283])).
% 2.34/2.55 tff(13285,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13246, 13284])).
% 2.34/2.55 tff(13286,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1792, 13285])).
% 2.34/2.55 tff(13287,plain,
% 2.34/2.55 (~b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[13260, 13286])).
% 2.34/2.55 tff(13288,plain,
% 2.34/2.55 (r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[80, 13287])).
% 2.34/2.55 tff(13289,plain,
% 2.34/2.55 (~r(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12449, 13288, 13284])).
% 2.34/2.55 tff(13290,plain,
% 2.34/2.55 (b(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2229, 13289])).
% 2.34/2.55 tff(13291,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13292,plain,
% 2.34/2.55 (((~b(z, s(s(s(s(z)))))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(13293,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[13292])).
% 2.34/2.55 tff(13294,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[13293, 13291])).
% 2.34/2.55 tff(13295,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(13296,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[13295, 13294])).
% 2.34/2.56 tff(13297,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[13296, 337, 13216, 2, 13038, 13286, 11268])).
% 2.34/2.56 tff(13298,plain,(~b(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(13299,plain,
% 2.34/2.56 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[548, 13298])).
% 2.34/2.56 tff(13300,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[13279, 13299, 13265])).
% 2.34/2.56 tff(13301,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2268, 13300])).
% 2.34/2.56 tff(13302,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(13303,plain,
% 2.34/2.56 (((~b(z, s(s(s(s(z)))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(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)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(13304,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[13303])).
% 2.34/2.56 tff(13305,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[13304, 13302])).
% 2.34/2.56 tff(13306,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(13307,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[13306, 13305])).
% 2.34/2.56 tff(13308,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[13307, 337, 13216, 13301, 13038, 13286, 13290])).
% 2.34/2.56 % SZS output end Proof
% 2.34/2.56 % E exiting
%------------------------------------------------------------------------------